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	<id>https://www.conservapedia.com/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=DanielB</id>
	<title>Conservapedia - User contributions [en]</title>
	<link rel="self" type="application/atom+xml" href="https://www.conservapedia.com/api.php?action=feedcontributions&amp;feedformat=atom&amp;user=DanielB"/>
	<link rel="alternate" type="text/html" href="https://www.conservapedia.com/Special:Contributions/DanielB"/>
	<updated>2026-10-17T06:12:52Z</updated>
	<subtitle>User contributions</subtitle>
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	<entry>
		<id>https://www.conservapedia.com/index.php?title=Talk:Derivative_(calculus)&amp;diff=495581</id>
		<title>Talk:Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Talk:Derivative_(calculus)&amp;diff=495581"/>
		<updated>2008-08-04T23:40:11Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;What a surprise--once again, a page in desperate need of revision. I'll do my best to delete absurd and meaningless statements, but someone else needs to come here and do a complete rewrite.--[[User:Mathoreilly|Mathoreilly]] 13:42, 2 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
So the page is at least a little less wrong now, but someone still needs to do something about the max/min section which is, to put it bluntly, very poorly written.--[[User:Mathoreilly|Mathoreilly]] 13:53, 2 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
:Someone other than you, apparently. Sorry, but I think a red link would be better than what you left us with.&lt;br /&gt;
&lt;br /&gt;
:I have taught SAT math and I earned AP credit for calculus. This was simply unacceptable quality. Do not edit any more math articles. --[[User:Ed Poor|Ed Poor]] &amp;lt;sup&amp;gt;[[User talk:Ed Poor|Talk]]&amp;lt;/sup&amp;gt; 14:41, 2 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
I have taken this out as suggested by Mathoeilly as it needs work, possiblly a different article,&lt;br /&gt;
&lt;br /&gt;
Thus the derivative is a measurement of how a function changes when the values of its inputs vary. Derivatives are helpful in determining the [[maximum|maxima]] and [[minimum|minima]] of a function. For example, taking the derivative of a quadratic function will yield a linear function. The points at which this function equals zero are called ''critical'' points. Maxima and minima can occur at critical points, and can be verified to be a maximum or minimum by the ''second derivative test''. The second derivative is used to determine the [[concavity]], or curved shape of the graph. Where the concavity is positive, the graph curves upwards, and could contain a relative minimum. Where the concavity is negative, the graph curves downwards, and could contain a relative maximum. Where the concavity equals zero is said to be a point of ''inflection,'' meaning that it is a point where the concavity could be changing. Also, differentials have numerous applications in physics.&lt;br /&gt;
&lt;br /&gt;
==The current article==&lt;br /&gt;
Okay I will make a list of questions about the article&lt;br /&gt;
#In what contacts do you mean &amp;quot;measure&amp;quot;? Measure has a very specific mathematical meaning how do you mean it.&lt;br /&gt;
#You link to tangent but if you look at the tangent article it discusses the tangent function and even then not in a way you can under stand the tangent function.&lt;br /&gt;
#&amp;quot;differentiation is the reverse process of integration&amp;quot; In all my years of doing maths I have never heard anyone use the word process unless they are discussing and actual physical process. I think the term you are looking for is operation.&lt;br /&gt;
#You then go on to talk about maxima and minima. This is all good but as we at now stage have found out anything about how to differentiate it is usless to the reader.&lt;br /&gt;
This article would be greatly help with some actual maths and some pictures (as no one who knows anything about maths have upload rights it is not going to happen.&lt;br /&gt;
I would make these changes myself but every time I have made one minor change to this article it is deleted or reverted ny Ed Poor, so I am not going to bother. This article is in no way going to help with your stated aims of creating a home schooling resource, but that is okay as I am not going to help either. [[User:DanielB|DanielB]] 19:40, 4 August 2008 (EDT)&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Talk:Limit_(mathematics)&amp;diff=487122</id>
		<title>Talk:Limit (mathematics)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Talk:Limit_(mathematics)&amp;diff=487122"/>
		<updated>2008-07-04T04:04:39Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;who writes this stuff??--[[User:Lemonpeel|Lemonpeel]] 21:41, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
The [[math]] articles were written by random editors of [[conservapedia]], I actually liked the earlier version of the article as it was easier to understand that the current version --&amp;lt;span style=&amp;quot;margin-top: -3px;&amp;quot;&amp;gt;&amp;amp;nbsp;[[Image:50 star flag.png|12px]]&amp;lt;/span&amp;gt;&amp;lt;span style=&amp;quot;position:relative; overflow:hidden; width:88px; height:15px; z-index:2;&amp;quot;&amp;gt; [[User:Deborah|Deborah]] [[Special:Contributions/Deborah|&amp;lt;font color=&amp;quot;gray&amp;quot;&amp;gt;(contributions)&amp;lt;/font&amp;gt;]] [[User_talk:Deborah|&amp;lt;font color=&amp;quot;darkslategray&amp;quot;&amp;gt;(talk)&amp;lt;/font&amp;gt;]]&amp;lt;/span&amp;gt; 22:05, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
:Deborah while the previous article was easier to read, it was easier to read because it was wrong. [[User:DanielB|DanielB]] 00:04, 4 July 2008 (EDT)&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487106</id>
		<title>Conway's game of life</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487106"/>
		<updated>2008-07-04T02:56:54Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Image:Animated glider emblem.gif|thumb|right|Glider pattern]]&lt;br /&gt;
&lt;br /&gt;
'''Conway's game of life''' (CGL) deals with a cellular automaton game called ''Life'', which was meant to simulate the ecology of one-celled creatures. It was invented by [[John Conway]] in 1970. &amp;lt;ref&amp;gt;[http://www.math.com/students/wonders/life/life.html Wonders of Math]&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
CGL is a simple game were by random squares on a grid are filled. These are deemed to be &amp;quot;alive&amp;quot;. Under a set rule based on the number of filled adjacent cells a cell either continues to live, die or is born.&lt;br /&gt;
&lt;br /&gt;
Despite being based on simple rules the outcome cannot be estimated in advance, only by running the simulation can you get any results. Despite it being based on a random begin and the rules being simple, patterns form very easily. One of the most common being the glider pattern.&lt;br /&gt;
&lt;br /&gt;
CGL have become increasingly studied in ecology as it give an interesting perspective on the behaviouer of ecosystems. It is often cited as an example of how [[evolution]] can occur in that with a simple rules and random starting positions complex patterns can form.&lt;br /&gt;
&lt;br /&gt;
In mathematics it is cited as an example of [[chaos]].&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
''The Science of Discworld 2: The Globe'' by Terry Pratchett, Ian Stewart and Jack Cohen, has a good easy to understand discrition of Conway's game of life.&lt;br /&gt;
&lt;br /&gt;
[[Category:mathematics]] [[Category:computers]] [[category:ecology]]&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
* [http://www.ibiblio.org/lifepatterns/ Conway's Game of Life]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=John_Conway&amp;diff=487105</id>
		<title>John Conway</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=John_Conway&amp;diff=487105"/>
		<updated>2008-07-04T02:56:26Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* References */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''John Conway''' is a professor of Finite Mathematics at Princeton University. He is most famous for his development of [[Conway's game of life]]. Conway is an atheist.&amp;lt;ref&amp;gt;[http://www.celebatheists.com/?title=John_Conway Celebrity atheists]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&amp;lt;references/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==External links==&lt;br /&gt;
* [http://www.ibiblio.org/lifepatterns/ Conway's Game of Life]&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
*[[Recreational mathematics]]&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT: Conway, John}}&lt;br /&gt;
[[category:mathematicians]]&lt;br /&gt;
[[category:atheists]]&lt;br /&gt;
[[Category:Academics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=John_Conway&amp;diff=487104</id>
		<title>John Conway</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=John_Conway&amp;diff=487104"/>
		<updated>2008-07-04T02:56:11Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''John Conway''' is a professor of Finite Mathematics at Princeton University. He is most famous for his development of [[Conway's game of life]]. Conway is an atheist.&amp;lt;ref&amp;gt;[http://www.celebatheists.com/?title=John_Conway Celebrity atheists]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&amp;lt;references/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
* [http://www.ibiblio.org/lifepatterns/ Conway's Game of Life]&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
*[[Recreational mathematics]]&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT: Conway, John}}&lt;br /&gt;
[[category:mathematicians]]&lt;br /&gt;
[[category:atheists]]&lt;br /&gt;
[[Category:Academics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487101</id>
		<title>Conway's game of life</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487101"/>
		<updated>2008-07-04T02:55:17Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Image:Animated glider emblem.gif|thumb|right|Glider pattern]]&lt;br /&gt;
&lt;br /&gt;
'''Conway's game of life''' (CGL) deals with a cellular automaton game called ''Life'', which was meant to simulate the ecology of one-celled creatures. It was invented by [[John Conway]] in 1970. &amp;lt;ref&amp;gt;[http://www.math.com/students/wonders/life/life.html Wonders of Math]&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
CGL is a simple game were by random squares on a grid are filled. These are deemed to be &amp;quot;alive&amp;quot;. Under a set rule based on the number of filled adjacent cells a cell either continues to live, die or is born.&lt;br /&gt;
&lt;br /&gt;
Despite being based on simple rules the outcome cannot be estimated in advance, only by running the simulation can you get any results. Despite it being based on a random begin and the rules being simple, patterns form very easily. One of the most common being the glider pattern.&lt;br /&gt;
&lt;br /&gt;
CGL have become increasingly studied in ecology as it give an interesting perspective on the behaviouer of ecosystems. It is often cited as an example of how [[evolution]] can occur in that with a simple rules and random starting positions complex patterns can form.&lt;br /&gt;
&lt;br /&gt;
In mathematics it is cited as an example of [[chaos]].&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;br /&gt;
&lt;br /&gt;
''The Science of Discworld 2: The Globe'' by Terry Pratchett, Ian Stewart and Jack Cohen, has a good easy to understand discrition of Conway's game of life.&lt;br /&gt;
&lt;br /&gt;
[[Category:mathematics]] [[Category:computers]] [[category:ecology]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487091</id>
		<title>Conway's game of life</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487091"/>
		<updated>2008-07-04T02:45:49Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Image:Animated glider emblem.gif|thumb|right|Glider pattern]]&lt;br /&gt;
&lt;br /&gt;
'''Conway's game of life''' deals with a cellular automaton game called ''Life'', which was meant to simulate the ecology of one-celled creatures. It was invented by [[John Conway]] in 1970. &amp;lt;ref&amp;gt;[http://www.math.com/students/wonders/life/life.html Wonders of Math]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=John_Conway&amp;diff=487090</id>
		<title>John Conway</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=John_Conway&amp;diff=487090"/>
		<updated>2008-07-04T02:45:37Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''John Conway''' is a professor of Finite Mathematics at Princeton University. He is most famous for his development of [[Conway's game of life]]. Conway is an atheist.&amp;lt;ref&amp;gt;[http://www.celebatheists.com/?title=John_Conway]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&amp;lt;references/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
* [http://www.ibiblio.org/lifepatterns/ Conway's Game of Life]&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
*[[Recreational mathematics]]&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT: Conway, John}}&lt;br /&gt;
[[category:mathematicians]]&lt;br /&gt;
[[category:atheists]]&lt;br /&gt;
[[Category:Academics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487089</id>
		<title>Conway's game of life</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487089"/>
		<updated>2008-07-04T02:44:47Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''Conway's game of life''' deals with a cellular automaton game called ''Life'', which was meant to simulate the ecology of one-celled creatures. It was invented by [[John Conway]] in 1970. &amp;lt;ref&amp;gt;[http://www.math.com/students/wonders/life/life.html Wonders of Math]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487088</id>
		<title>Conway's game of life</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487088"/>
		<updated>2008-07-04T02:44:31Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''Conway's game of life''' deals with a cellular automaton game called ''Life'', which was meant to simulate the ecology of one-celled creatures. It was invented by [[Joh Conaway]] in 1970. &amp;lt;ref&amp;gt;[http://www.math.com/students/wonders/life/life.html Wonders of Math]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
{{reflist}}&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487086</id>
		<title>Conway's game of life</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conway%27s_game_of_life&amp;diff=487086"/>
		<updated>2008-07-04T02:43:14Z</updated>

		<summary type="html">&lt;p&gt;DanielB: Starte dfixing&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Conway's game of life deals with a cellular automaton game called ''Life'', which was meant to simulate the ecology of one-celled creatures but is mostly a lot of fun. &amp;lt;ref&amp;gt;&amp;quot;Life was invented by the mathematician John Conway in 1970. He choose the rules carefully after trying many other possibilities, some of which caused the cells to die too fast and others which caused too many cells to be born.&amp;quot; [http://www.math.com/students/wonders/life/life.html Wonders of Math]&amp;lt;/ref&amp;gt;&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=John_Conway&amp;diff=487085</id>
		<title>John Conway</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=John_Conway&amp;diff=487085"/>
		<updated>2008-07-04T02:42:02Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[Image:Animated glider emblem.gif|thumb|right|Glider pattern]]&lt;br /&gt;
'''John Conway''' is a professor of Finite Mathematics at Princeton University. He is most famous for his development of [[Conway's game of life]]. Conway is an atheist.[http://www.celebatheists.com/?title=John_Conway]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&amp;lt;references/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
* [http://www.ibiblio.org/lifepatterns/ Conway's Game of Life]&lt;br /&gt;
&lt;br /&gt;
==See also==&lt;br /&gt;
*[[Recreational mathematics]]&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT: Conway, John}}&lt;br /&gt;
[[category:mathematicians]]&lt;br /&gt;
[[category:atheists]]&lt;br /&gt;
[[Category:Academics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487082</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487082"/>
		<updated>2008-07-04T02:38:00Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Trigonometry */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics has developed historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see: [[Conservapedia:Mathematics articles by schooling level]].&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Limit (mathematics)|Limits]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Matrix|Matricies]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Guass-Jordan elimination]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Riemann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtions]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtions]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487081</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487081"/>
		<updated>2008-07-04T02:36:49Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics has developed historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see: [[Conservapedia:Mathematics articles by schooling level]].&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Limit (mathematics)|Limits]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Matrix|Matricies]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Guass-Jordan elimination]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Riemann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487080</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487080"/>
		<updated>2008-07-04T02:36:34Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Linear equations */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics has developed historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see: [[Conservapedia:Mathematics articles by schooling level]].&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Limit (mathematics)|Limits]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Matrix|Matricies]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Guass-Jordan elimination]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Riemann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Slope&amp;diff=487069</id>
		<title>Slope</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Slope&amp;diff=487069"/>
		<updated>2008-07-04T02:19:08Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Introduction to derivative */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''Slope''' is the steepness of a [[line]].  A positive slope rises; a negative slope falls.  Another term for slope is gradient.&lt;br /&gt;
&lt;br /&gt;
For a straight line, the slope (m) is constant and represented by the difference in the vertical direction (y) divided by the difference in the horizontal direction (x):&lt;br /&gt;
&lt;br /&gt;
:: &amp;lt;math&amp;gt;m = \frac{\Delta y}{\Delta x}&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The delta, Δ, represents the difference in values between any two points in the x or y direction for straight line.  For a [[curve]], the delta, Δ, represents the difference in values for two points in very close proximity to each other.&lt;br /&gt;
&lt;br /&gt;
For a straight line, another way of representing the slope (m) is as follows:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;m = \frac{y_2 - y_1}{x_2 - x_1}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where the two points are located at (x&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, y&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;) and (x&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, y&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
===Introduction to derivative===&lt;br /&gt;
&lt;br /&gt;
If a function has value &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;f(x+h)&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;x+h&amp;lt;/math&amp;gt; with &amp;lt;math&amp;gt;h&amp;gt;0&amp;lt;/math&amp;gt; than the slope of the line joining &amp;lt;math&amp;gt;(x,f(x))&amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;(x+h,f(x+h))&amp;lt;/math&amp;gt; is,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
The slope of the line that meets (is tangential to) &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the limit as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero, or,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
which is denoted &amp;lt;math&amp;gt;f'(x)&amp;lt;/math&amp;gt;, which is called the [[derivative]] of &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
[[Category:Algebra]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=487064</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=487064"/>
		<updated>2008-07-04T02:15:10Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics the '''derivative''' is the rate of change of a function with respect to one of its variables. For example, if &amp;lt;math&amp;gt;r(t)&amp;lt;/math&amp;gt; denotes the position of a particle on a line as a function of time, the derivative of &amp;lt;math&amp;gt;r&amp;lt;/math&amp;gt; with respect to the time variable &amp;lt;math&amp;gt;t&amp;lt;/math&amp;gt; is the rate of change of the particle's position with respect to time, i.e., the speed of the particle. Similarly, the derivative of the particle's speed with respect to time corresponds to the particle's acceleration. Other examples of derivatives in physics abound: for example, the derivative can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Differentiation is one of two fundamental operations in [[calculus]], the other being [[integration]].&lt;br /&gt;
&lt;br /&gt;
For a real-valued function &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt; of one variable, the derivative of &amp;lt;math&amp;gt;f&amp;lt;/math&amp;gt; corresponds to the [[slope]] of the tangent line to the graph of ''f'' at ''x''.&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]] {{fact}}.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over the interval &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative is obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth. The derivatives are termed the n-th order derivative e.g, second order derivative, third order derivative. &lt;br /&gt;
&lt;br /&gt;
A common alternative notation is, &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=f''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=f'''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}y}{dx^{n}}=f^{n}(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dashes are actually roman numerals: the symbol for the forth order derivative would be a slanted IV.&lt;br /&gt;
 &lt;br /&gt;
Continuing our earlier example; &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the second derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}} = \frac{d}{dx}(6 x+2)=6&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}} = \frac{d}{dx}(6)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
All subsequent derivatives would be zero. For any [[polynomial]] of order n-1, &amp;lt;math&amp;gt;P_{n-1}(x)&amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}}{dx^{n}}P_{n-1}(x)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Other than the second derivative these have no real applications{{fact}}. A function which has derivatives of all orders is called a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
*[[Partial derivatives]]&lt;br /&gt;
*[[Applications of derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Slope&amp;diff=487061</id>
		<title>Slope</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Slope&amp;diff=487061"/>
		<updated>2008-07-04T02:11:09Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Introduction to derivative */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''Slope''' is the steepness of a [[line]].  A positive slope rises; a negative slope falls.  Another term for slope is gradient.&lt;br /&gt;
&lt;br /&gt;
For a straight line, the slope (m) is constant and represented by the difference in the vertical direction (y) divided by the difference in the horizontal direction (x):&lt;br /&gt;
&lt;br /&gt;
:: &amp;lt;math&amp;gt;m = \frac{\Delta y}{\Delta x}&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The delta, Δ, represents the difference in values between any two points in the x or y direction for straight line.  For a [[curve]], the delta, Δ, represents the difference in values for two points in very close proximity to each other.&lt;br /&gt;
&lt;br /&gt;
For a straight line, another way of representing the slope (m) is as follows:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;m = \frac{y_2 - y_1}{x_2 - x_1}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where the two points are located at (x&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, y&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;) and (x&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, y&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
===Introduction to derivative===&lt;br /&gt;
&lt;br /&gt;
If a function has value &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;f(x+h)&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;x+h&amp;lt;/math&amp;gt; with &amp;lt;math&amp;gt;h&amp;gt;0&amp;lt;/math&amp;gt; than the slope of the line joining &amp;lt;math&amp;gt;(x,f(x))&amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;(x+h,f(x+h))&amp;lt;/math&amp;gt; is,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Therefor the slope of the line that meet (is tangential to) &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the limit as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero, or,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
which is denoted &amp;lt;math&amp;gt;f'(x)&amp;lt;/math&amp;gt;, which is called the [[derivative]] of &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
[[Category:Algebra]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Slope&amp;diff=487060</id>
		<title>Slope</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Slope&amp;diff=487060"/>
		<updated>2008-07-04T02:10:42Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''Slope''' is the steepness of a [[line]].  A positive slope rises; a negative slope falls.  Another term for slope is gradient.&lt;br /&gt;
&lt;br /&gt;
For a straight line, the slope (m) is constant and represented by the difference in the vertical direction (y) divided by the difference in the horizontal direction (x):&lt;br /&gt;
&lt;br /&gt;
:: &amp;lt;math&amp;gt;m = \frac{\Delta y}{\Delta x}&amp;lt;/math&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The delta, Δ, represents the difference in values between any two points in the x or y direction for straight line.  For a [[curve]], the delta, Δ, represents the difference in values for two points in very close proximity to each other.&lt;br /&gt;
&lt;br /&gt;
For a straight line, another way of representing the slope (m) is as follows:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;m = \frac{y_2 - y_1}{x_2 - x_1}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where the two points are located at (x&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;, y&amp;lt;sub&amp;gt;1&amp;lt;/sub&amp;gt;) and (x&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;, y&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt;).&lt;br /&gt;
&lt;br /&gt;
===Introduction to derivative===&lt;br /&gt;
&lt;br /&gt;
If a function has value &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; and &amp;lt;math&amp;gt;f(x+h)&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;x+h&amp;lt;/math&amp;gt; with &amp;lt;math&amp;gt;h&amp;gt;0&amp;lt;/math&amp;gt; than the gradient of the line joining &amp;lt;math&amp;gt;(x,f(x))&amp;lt;/math&amp;gt; to &amp;lt;math&amp;gt;(x+h,f(x+h))&amp;lt;/math&amp;gt; is,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
Therefor the gradient of the line that meet (is tangential to) &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is the limit as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero, or,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\lim_{h\rightarrow0}\frac{f(x+h)-f(x)}{h},&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
which is denoted &amp;lt;math&amp;gt;f'(x)&amp;lt;/math&amp;gt;, which is called the [[derivative]] of &amp;lt;math&amp;gt;f(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
[[Category:Algebra]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Gradient_(two_points)&amp;diff=487056</id>
		<title>Gradient (two points)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Gradient_(two_points)&amp;diff=487056"/>
		<updated>2008-07-04T02:09:52Z</updated>

		<summary type="html">&lt;p&gt;DanielB: Redirecting to Slope&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;#REDIRECT [[Slope]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Gradient&amp;diff=487054</id>
		<title>Gradient</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Gradient&amp;diff=487054"/>
		<updated>2008-07-04T02:09:13Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{math-a}}&lt;br /&gt;
&lt;br /&gt;
In [[mathematics]], the gradient of a real-valued differentiable function &amp;lt;math&amp;gt;f(x_1,...,x_n)&amp;lt;/math&amp;gt; at a point &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt; is a vector in &amp;lt;math&amp;gt;R^n&amp;lt;/math&amp;gt; which points in the direction in which &amp;lt;math&amp;gt;f&amp;lt;/math&amp;gt; increases most rapidly at &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;. The magnitude of the gradient at &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt; is equal to the maximum directional derivative of &amp;lt;math&amp;gt;f&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
More precisely, we define the gradient, &amp;lt;math&amp;gt;\nabla f&amp;lt;/math&amp;gt; of &amp;lt;math&amp;gt;f&amp;lt;/math&amp;gt; to be the vector-field: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
\nabla f = (\frac{\partial f}{\partial x_1},...,\frac{\partial f}{\partial x_n})&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;u&amp;lt;/math&amp;gt; is a unit vector in &amp;lt;math&amp;gt;R^n&amp;lt;/math&amp;gt;, then, by the chain rule, the directional derivative of &amp;lt;math&amp;gt;f&amp;lt;/math&amp;gt; in the direction of &amp;lt;math&amp;gt;u&amp;lt;/math&amp;gt; is simply the dot product:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
\nabla f \cdot u&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Evidently by the Cauchy-Schwartz inequality, the directional derivative in the direction &amp;lt;math&amp;gt;u&amp;lt;/math&amp;gt; is maximal in the direction of the gradient, and equal to &amp;lt;math&amp;gt;||\nabla f||&amp;lt;/math&amp;gt; for &amp;lt;math&amp;gt;u&amp;lt;/math&amp;gt; a unit vector in the direction of the gradient.&lt;br /&gt;
&lt;br /&gt;
==Properties of the Gradient==&lt;br /&gt;
&lt;br /&gt;
If &amp;lt;math&amp;gt;f&amp;lt;/math&amp;gt; is a differentiable function with smooth level sets &amp;lt;math&amp;gt;f^{-1}(c)&amp;lt;/math&amp;gt;, then the gradient vector field &amp;lt;math&amp;gt;\nabla f&amp;lt;/math&amp;gt; is perpendicular to the level sets of &amp;lt;math&amp;gt;f&amp;lt;/math&amp;gt;. For fix a level set &amp;lt;math&amp;gt;S = f^{-1}(c)&amp;lt;/math&amp;gt;, and let &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; be a vector tangent to &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;. Then we can find a curve &amp;lt;math&amp;gt;\gamma(t)&amp;lt;/math&amp;gt; on &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; with &amp;lt;math&amp;gt;\gamma'(0) = v&amp;lt;/math&amp;gt;. Now&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
f\circ\gamma(t) = c&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
since &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is a level set. Taking derivatives of both sides and applying the chain rule, we get that &lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
\nabla f\cdot \gamma'(0) = \nabla f\cdot v = 0&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Thus, &amp;lt;math&amp;gt;\nabla f&amp;lt;/math&amp;gt; is perpendicular to &amp;lt;math&amp;gt;v&amp;lt;/math&amp;gt; at &amp;lt;math&amp;gt;p&amp;lt;/math&amp;gt;, i.e., the gradient of &amp;lt;math&amp;gt;f&amp;lt;/math&amp;gt; is perpendicular to the level sets of &amp;lt;math&amp;gt;f&amp;lt;/math&amp;gt;.&lt;br /&gt;
[[Category:mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487053</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487053"/>
		<updated>2008-07-04T02:08:56Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics has developed historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see: [[Conservapedia:Mathematics articles by schooling level]].&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Limit (mathematics)|Limits]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Riemann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Characteristic_polynomial&amp;diff=487046</id>
		<title>Characteristic polynomial</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Characteristic_polynomial&amp;diff=487046"/>
		<updated>2008-07-04T02:04:49Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The '''characteristic polynomial''' of a square [[matrix]] &amp;lt;math&amp;gt;A&amp;lt;/math&amp;gt; is given by,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f(\lambda) = \det(A-\lambda I)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where &amp;lt;math&amp;gt;I&amp;lt;/math&amp;gt; is the [[identity matrix]]. The zeros of this polynomial are the [[eigenvalue]]s of the matrix.&lt;br /&gt;
&lt;br /&gt;
[[Category:Linear algebra]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487045</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487045"/>
		<updated>2008-07-04T02:03:55Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics has developed historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see: [[Conservapedia:Mathematics articles by schooling level]].&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Limit (mathematics)|Limits]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Riemann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487043</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487043"/>
		<updated>2008-07-04T02:02:01Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics has developed historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Limit (mathematics)|Limits]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Riemann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487041</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487041"/>
		<updated>2008-07-04T02:01:00Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics has developed historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Limit (mathematics)|Limits]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487038</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=487038"/>
		<updated>2008-07-04T02:00:22Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Differential calculus */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics has developed historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Limit (mathematics)|Limits]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Richard_Lenski&amp;diff=486925</id>
		<title>Richard Lenski</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Richard_Lenski&amp;diff=486925"/>
		<updated>2008-07-04T00:08:02Z</updated>

		<summary type="html">&lt;p&gt;DanielB: Made table a little more modest we don't need to shout.&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;'''Richard Lenski''' is a professor of microbial [[ecology]] at Michigan State [[University]].  He holds a [[doctorate]] from the [[University of North Carolina]] and a B.A. from Oberlin College but does not disclose his fields for those degrees on his own biographical sketch.&amp;lt;ref&amp;gt;https://www.msu.edu/~lenski/&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Richard Lenski is best known for his questionable claim to have observed the [[theory of evolution]] in practice, saying that [[E. coli]] bacteria made minor changes in a long-term laboratory study, and insisting that it was not due to contamination.  The 2008 paper he co-authored was [[peer review]]ed in a mere 14 days, sparking obvious questions&amp;lt;ref&amp;gt;See [[Conservapedia talk:Lenski dialog]].&amp;lt;/ref&amp;gt; about the thoroughness of the review.&lt;br /&gt;
&lt;br /&gt;
When challenged, Lenski displayed several examples of irrational [[Professor values|behavior]], thrice referring to the challenges as [[slander]], yet has filed no [[lawsuit]] charging that (or [[libel]]). [[Truth]] offers total legal protection from accusations of libel. He has also displayed annoyance, arrogance, and [[elitism]] when asked to release the information.&amp;lt;ref&amp;gt;See [[Conservapedia:Lenski_dialog#Second_reply|Lenski's second reply to Andrew Schlafly]]&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
When Richard Lenski received a public request for the [[data]] underlying for his published claims, he did not provide the actual data even though his study was taxpayer-funded. Lenski's refusal to provide the raw data even to fellow [[Darwinist]]s is telling, and makes it clear that he will not allow his claims to be tested by [[Creation science|open-minded scientists]].&lt;br /&gt;
&lt;br /&gt;
Undisclosed data from the central claims in Lenski's 2008 paper are noted below (pp. 2-3 from paper, superscripts omitted):&amp;lt;ref&amp;gt;For those wishing to review the paper personally it may be found at [http://myxo.css.msu.edu/lenski/pdf/2008,%20PNAS,%20Blount%20et%20al.pdf this link] from Lenski's website.&amp;lt;/ref&amp;gt;&amp;lt;ref&amp;gt;A Lenski defender has asserted that this table format is copyrighted under [[GFDL]], which imposes overly complex rules for reuse.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;includeonly&amp;gt;&lt;br /&gt;
{{DEFAULTSORT:{{PAGENAME}}}}&lt;br /&gt;
&amp;lt;/includeonly&amp;gt;&lt;br /&gt;
__NOTOC__&lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=2 cellpadding=2&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top bgcolor=#003366 align=center&amp;gt;&amp;lt;font color=&amp;quot;#f6f7ff&amp;quot; size=&amp;quot;+1&amp;quot;&amp;gt;Undisclosed Data&amp;lt;/font&amp;gt;&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top bgcolor=#000000 align=center&amp;gt;&amp;lt;font color=&amp;quot;#f6f7ff&amp;quot; size=&amp;quot;+1&amp;quot;&amp;gt;Our Questions about the missing data&amp;lt;/font&amp;gt;&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Visual inspection====&lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Evolution of Cit Function in Population Ara-3. The LTEE populations are transferred daily into fresh medium, and the turbidity of each is checked visually at that time. ...&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Data on these observations?&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Turbidity==== &lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
...the cultures are only slightly turbid when transferred. Occasional contaminants that grow on citrate have been seen over the 20 years of this experiment.&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Data? When and how many?&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Contaminants???==== &lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
These contaminated cultures reach much higher turbidity owing to the high concentration of [[citrate]] in the medium, which allows the contaminants to reach high density. (When contamination occurs, the affected population is restarted from the latest frozen sample.) &lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Data for when that occurred, and how often?&lt;br /&gt;
&lt;br /&gt;
A Richard Lenski defender says, &amp;quot;If interested in a thorough review, contact the group directly, with a legitimate request for data.  Otherwise, the disclaimer is a more than adequate description of the sample handling process.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
In fact, two requests were made directly to Lenski for data, without success. His [[Conservapedia:Lenski dialog#Second_Reply|second response]] was rude and insulting.&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====The Numbers Please?====&lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
After 33,127 generations, one population, designated Ara-3, displayed significantly elevated turbidity that continued to rise for several days (Fig. 1).&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Higher resolution data underlying figure not provided despite request.&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====More missing Numbers==== &lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
A number...&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Data? How many? Statistically significant?&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====We're Professional Scientists====&lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
of Cit clones were isolated from the population and checked for phenotypic markers characteristic of the ancestral E. coli strain used to start the LTEE: all&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Data? How many? Statistically significant?&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Missing Characteristics====&lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
...were Ara, T5-sensitive, and T6-resistant, as expected (2)&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Data about these and other characteristics?&lt;br /&gt;
&lt;br /&gt;
A Richard Lenski defender says, &amp;quot;Interested parties should consult the literature on these topics.  It is not within the scope of this paper to address the significance of these markers.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
What is missing from disclosure are the data that the markers were actually observed in a reliable and conclusive manner in this study.&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====DNA====&lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
DNA sequencing also showed...&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
DATA??&lt;br /&gt;
&lt;br /&gt;
A Richard Lenski defender says, &amp;quot;The inclusion of this data would be considerably more extensive than appropriate for the inclusion in this paper.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
No one asked for the data to be printed in the paper. What is missing is disclosure of the data on the website, or upon public request.&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====More missing data==== &lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
...that Cit clones have the same mutations in the pykF and nadR genes as do clones from earlier generations of the Ara-3 population, ... &lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Data about these and other characteristics?&lt;br /&gt;
&lt;br /&gt;
A Lenski defender cites to general information unrelated to this study: Available in other publications,&lt;br /&gt;
pykF &amp;lt;ref&amp;gt;[http://www.ihop-net.org/UniPub/iHOP/gs/519955.html &amp;quot;IHOP-pykF&amp;quot;]&amp;lt;/ref&amp;gt; and&lt;br /&gt;
nadR &amp;lt;ref&amp;gt;[http://www.ihop-net.org/UniPub/iHOP/mgi/447129.html &amp;quot;IHOP-nadR&amp;quot;]&amp;lt;/ref&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
A Richard Lenski defender also cites an earlier claim (perhaps also unsupported by public release of the data) by Lenski's group: See also the reference for the sequence identification which Blount ''et al.'' list as reference #30 in their paper: Woods, R., D. Schneider, C. L. Winkworth, M. A. Riley, and R. E. Lenski. 2006. Tests of parallel molecular evolution in a long-term experiment with Escherichia coli. PNAS, USA 103:9107-9112.&amp;lt;ref&amp;gt;http://www.pnas.org/cgi/content/abstract/0602917103v1&amp;lt;/ref&amp;gt;.&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====More missing data==== &lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
...and each of these mutations distinguishes this population from all the others (30). &lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Data distinguishing &amp;quot;This population from all the others&amp;quot;?&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
====Fast Tracked====&lt;br /&gt;
&amp;lt;TABLE width=100% cellspacing=10&amp;gt;&lt;br /&gt;
&amp;lt;TR&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
Therefore, the Cit variant arose within the LTEE and is not a contaminant.&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;TD width=50% valign=top&amp;gt;&lt;br /&gt;
The astoundingly short 14-day [[peer review | PEER REVIEW]] period, measured from the day the paper was sent out for review to the day of formal contribution by Lenski after acceptance, raises questions as to whether there was any meaningful peer review of this at all.&lt;br /&gt;
&amp;lt;/TD&amp;gt;&amp;lt;/TR&amp;gt;&amp;lt;/table&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== ==&lt;br /&gt;
Lenski's paper was published in the Proceedings of the [[National Academy of Sciences]], a professional society of scientists with a strong bias towards [[atheism]] and [[evolutionism]]. &amp;lt;ref&amp;gt;http://www.stephenjaygould.org/ctrl/news/file002.html&amp;lt;/ref&amp;gt; &amp;lt;ref&amp;gt;http://www.answersingenesis.org/docs/3506.asp&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Lenski's work has been criticized in the past also.  In a paper Lenski published in ''Nature'' in May 8, 2003 entitled &amp;quot;The Evolutionary Origin of Complex Features,&amp;quot; he described a computer simulation that contained no actual biology.  In fact, the discussion section of the paper stated:&lt;br /&gt;
&lt;br /&gt;
:&amp;quot;Some readers might suggest that we 'stacked the deck' by studying the evolution of a complex feature that could be built on simpler functions that were also useful. However, that is precisely what evolutionary theory requires ....&amp;quot; &lt;br /&gt;
&lt;br /&gt;
Dr. William Dembski explained, &amp;quot;In other words, the computer programmers built into the simulation what they thought evolution needed to make it work. The validity of this study therefore depends on whether the simulation faithfully models biological reality.&amp;quot;&amp;lt;ref&amp;gt;http://www.designinference.com/documents/2003.09.UncDiss_Intro_Contribs.pdf&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
*[[Conservapedia:Lenski dialog]] (letters requesting data, and Lenski's responses)&lt;br /&gt;
*[[Conservapedia talk:Lenski dialog]] (discussion of Lenski controversy&amp;lt;ref&amp;gt;See [[Liberal style]] point 1&amp;lt;/ref&amp;gt;)&lt;br /&gt;
[[Category:Biology]]&lt;br /&gt;
[[Category:Scientists]]&lt;br /&gt;
[[Category:Evolution]]&lt;br /&gt;
[[Category:Deceit]]&lt;br /&gt;
&lt;br /&gt;
==References==&lt;br /&gt;
&amp;lt;references/&amp;gt;&lt;br /&gt;
&lt;br /&gt;
{{DEFAULTSORT:Lenski, Richard}}&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486912</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486912"/>
		<updated>2008-07-03T23:50:28Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative is obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth. The derivatives are termed the n-th order derivative e.g, second order derivative, third order derivative. &lt;br /&gt;
&lt;br /&gt;
A common alternative notation is, &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=f''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=f'''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}y}{dx^{n}}=f^{n}(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dashes are actually roman numerals: the symbol for the forth order derivative would be a slanted IV.&lt;br /&gt;
 &lt;br /&gt;
Picking up our earlier example; &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the second derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}} = \frac{d}{dx}(6 x+2)=6&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}} = \frac{d}{dx}(6)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
All subsequent derivatives would be zero. For any [[polynomial]] of order n-1, &amp;lt;math&amp;gt;P_{n-1}(x)&amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}}{dx^{n}}P_{n-1}(x)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Other than the second derivative these have no real applications{{fact}}. A function which is differentiable infinite times is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
*[[Partial derivatives]]&lt;br /&gt;
*[[Applications of derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486911</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486911"/>
		<updated>2008-07-03T23:50:07Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Important differentiation rules */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative is obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth. The derivatives are termed the n-th order derivative e.g, second order derivative, third order derivative. &lt;br /&gt;
&lt;br /&gt;
A common alternative notation is, &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=f''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=f'''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}y}{dx^{n}}=f^{n}(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dashes are actually roman numerals: the symbol for the forth order derivative would be a slanted IV.&lt;br /&gt;
 &lt;br /&gt;
Picking up our earlier example; &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the second derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}} = \frac{d}{dx}(6 x+2)=6&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}} = \frac{d}{dx}(6)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
All subsequent derivatives would be zero. For any [[polynomial]] of order n-1, &amp;lt;math&amp;gt;P_{n-1}(x)&amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}}{dx^{n}}P_{n-1}(x)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Other than the second derivative these have no real applications{{fact}}. A function which is differentiable infinite times is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
*[[Partial derivatives]]&lt;br /&gt;
*[[Applications of derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486909</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486909"/>
		<updated>2008-07-03T23:49:04Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative is obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth. The derivatives are termed the n-th order derivative e.g, second order derivative, third order derivative. &lt;br /&gt;
&lt;br /&gt;
A common alternative notation is, &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=f''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=f'''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}y}{dx^{n}}=f^{n}(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dashes are actually roman numerals: the symbol for the forth order derivative would be a slanted IV.&lt;br /&gt;
 &lt;br /&gt;
Picking up our earlier example; &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the second derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}} = \frac{d}{dx}(6 x+2)=6&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}} = \frac{d}{dx}(6)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
All subsequent derivatives would be zero. For any [[polynomial]] of order n-1, &amp;lt;math&amp;gt;P_{n-1}(x)&amp;lt;/math&amp;gt;,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}}{dx^{n}}P_{n-1}(x)=0&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Other than the second derivative these have no real applications{{fact}}. A function which is differentiable infinite times is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
*[[Partial derivatives]]&lt;br /&gt;
*[[Applications of derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486906</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486906"/>
		<updated>2008-07-03T23:45:00Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Higher order derivatives */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative is obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth. The derivatives are termed the n-th order derivative e.g, second order derivative, third order derivative. &lt;br /&gt;
&lt;br /&gt;
A common alternative notation is, &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=f''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=f'''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}y}{dx^{n}}=f^{n}(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dashes are actually roman numerals: the symbol for the forth order derivative would be a slanted IV.&lt;br /&gt;
 &lt;br /&gt;
Picking up our earlier example;&lt;br /&gt;
&lt;br /&gt;
Other than the second derivative these have no real applications{{fact}}. A function which is differentiable infinite times is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
*[[Partial derivatives]]&lt;br /&gt;
*[[Applications of derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486901</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486901"/>
		<updated>2008-07-03T23:39:48Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Higher order derivatives */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative is obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth. The derviatives are termed the n-th order derivative e.g, second order derivative, third order derivative. &lt;br /&gt;
&lt;br /&gt;
A common alternative notation is, &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=f''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=f'''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}y}{dx^{n}}=f^{n}(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dashes are actually roman numerals the symbol for the forth order derivative would be a slanted IV.&lt;br /&gt;
 &lt;br /&gt;
Other than the second derivative these have no real applications{{fact}}. A function which is differentiable infinite times is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
*[[Partial derivatives]]&lt;br /&gt;
*[[Applications of derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486897</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486897"/>
		<updated>2008-07-03T23:38:14Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Higher order derivatives */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative is obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth. The derviatives are termed the n-th order derivative e.g, second order derivative, third order derivative. &lt;br /&gt;
&lt;br /&gt;
A common alternative notation is, &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=f''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=f'''(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{n}y}{dx^{n}}=f^{n}(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The dashes actually roman numerals the symbol for the forth order derivative would be a slanted IV.&lt;br /&gt;
 &lt;br /&gt;
Other than the second derivative these have no real applications{{fact}}. A function which is differentiable infinite times is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
*[[Partial derivatives]]&lt;br /&gt;
*[[Applications of derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486891</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486891"/>
		<updated>2008-07-03T23:27:11Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* See Also */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative are obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth.&lt;br /&gt;
&lt;br /&gt;
Other than the second derivative these have no real applications. A function which is infinitly time differentiable is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
[[Partial derivatives]]&lt;br /&gt;
[[Applications of derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486890</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486890"/>
		<updated>2008-07-03T23:26:40Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Higher order derivatives */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative are obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth.&lt;br /&gt;
&lt;br /&gt;
Other than the second derivative these have no real applications. A function which is infinitly time differentiable is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
[[Partial derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486889</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486889"/>
		<updated>2008-07-03T23:26:26Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Higher order derivatives */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative are obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth.&lt;br /&gt;
&lt;br /&gt;
Other than the second derivative these have no real applications. A function which is infinitly time differntiabe is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
[[Partial derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486888</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486888"/>
		<updated>2008-07-03T23:26:16Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Important differentiation rules */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
==Higher order derivatives==&lt;br /&gt;
&lt;br /&gt;
A higher order derivative are obtained by repeating derivatives,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}\left(\frac{dy}{dx}\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d^{3}y}{dx^{3}}=\frac{d}{dx}\left(\frac{d^{2}y}{dx^{2}}\right)=\frac{d}{dx}\left(\frac{d}{dx}\left(\frac{dy}{dx}\right)\right)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
and so forth.&lt;br /&gt;
&lt;br /&gt;
Other than the seond derivative these have no real applications. A function which is infinitly time differntiabe is termed a [[smooth function]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
[[Partial derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486885</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486885"/>
		<updated>2008-07-03T23:20:22Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics has developed historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Talk:Conservapedia_challenge&amp;diff=486883</id>
		<title>Talk:Conservapedia challenge</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Talk:Conservapedia_challenge&amp;diff=486883"/>
		<updated>2008-07-03T23:17:56Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;A challenge! Very well, Sir, I accept!&lt;br /&gt;
&lt;br /&gt;
I am not a rich man and would be unable to handle all the data accumulated over twenty years. Neither do I think it acceptable to enjoin a publically funded organization to spend the large sums required to send such a large amount of data without a defined public benefit.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Let us, then, agree a hypothesis that can be tested by ' 'some' ', of Prof. Lenski's unpublished data.  I will then procure from said Professor either:&lt;br /&gt;
1) That very data, which I will then deliver to you, or&lt;br /&gt;
2) An admission from the Professor that he does not have that data&lt;br /&gt;
&lt;br /&gt;
If I succeed you will:&lt;br /&gt;
1) procure me one pint of Fuller's &amp;quot;London Pride&amp;quot; at the Nicholson's pub in the Strand, London, and display a picture of me drinking it on the front page of Conservapedia.&lt;br /&gt;
2) Publish a statement on the front page of Conservapedia stating that you accept Professor Lenski's honesty and professionalism.&lt;br /&gt;
&lt;br /&gt;
I await:&lt;br /&gt;
1) Your hypothesis&lt;br /&gt;
2) The data that would test it&lt;br /&gt;
3) Your &amp;quot;prize&amp;quot; should I fail&lt;br /&gt;
&lt;br /&gt;
Regards&lt;br /&gt;
Tony Lloyd (User:TonyLloyd&lt;br /&gt;
&lt;br /&gt;
: Your &amp;quot;offer&amp;quot; is fascinating but also self-contradictory.  On the one hand you imply that there are voluminous data (&amp;quot;spend the large sums required to send such a large amount of data&amp;quot;), but on the other hand you suggest that Lenski may not have any such data!  You also seem to misunderstand or ignore the purpose and benefits of public scrutiny, as the data are not merely for me (&amp;quot;your hypothesis&amp;quot; and &amp;quot;data that would test it&amp;quot;) but for all the public who paid for the data.--[[User:Aschlafly|Aschlafly]] 13:18, 3 July 2008 (EDT)&lt;br /&gt;
::As I have asked elsewhere Mr Schlafly I really do think you need to clarify [[Talk:Main_Page#Lenski.27s_data  | nature of the data requested and who would examine it]], and explain if you accept the [[Talk:Main_Page#Legal_means_to_get_Lenski.27s_data_2 | data are represented by the organisms]] (and if you think the data are not represented by the organisms explain why not.)--[[User:British_cons|British_cons]] [[User_talk:British_cons|(talk)]] 13:28, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
At least one blogger has already claimed to have won the challenge: [http://nolatitude.blogspot.com/2008/07/conservapedia-stubborn-idiocy-in-action.html No Latitude]. He cites and links to the following data:&lt;br /&gt;
http://myxo.css.msu.edu/lenski/pdf/2008,%20PNAS,%20Blount%20et%20al.pdf&lt;br /&gt;
http://www.pnas.org/content/103/24/9107.full.pdf+html&lt;br /&gt;
http://myxo.css.msu.edu/lenski/pdf/2004,%20Plant%20Breeding%20Reviews,%20Lenski.pdf&lt;br /&gt;
http://myxo.css.msu.edu/lenski/pdf/2003,%20JME,%20Lenski%20et%20al.pdf&lt;br /&gt;
http://myxo.css.msu.edu/lenski/pdf/2003,%20PNAS,%20Cooper%20et%20al.pdf&lt;br /&gt;
&lt;br /&gt;
Of these, the last is particularly data-rich.&lt;br /&gt;
&lt;br /&gt;
: The missing data are very specific.  The above citation list is a common tactic of distraction:  try to obscure by burying the reader with volumes of meaningless or less meaningful info.  Most of the dates on those cites are years ago, predating when key data could have even occurred.--[[User:Aschlafly|Aschlafly]] 14:05, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::''Most of the dates on those cites are years ago'' But not ALL of them, right? What about those citations which do not predate what you are looking for? Also, the Lenski dialogue now exists on several talk pages besides this one, some of them archived. I'm a busy person and do not have time to go hunting around through dozens if not hundreds of posts. Would it be too much of an imposition to ask you to state here, in a concise manner, what data exactly that would satisfy your request? - I say this in part because many of your interlocutors are trying to make YOU look unreasonable by making it appear as though you want Lenski to ship you on old mustard jar full of e coli (yes, I'm exaggerating)...I think it would do this discussion some good to refocus it on a short list of exactly what it is you're looking for...[[User:AliceBG|AliceBG]] 14:19, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::The oldest paper there is from generation 20,000.[[User:JPohl|JPohl]] 14:20, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
There is no contradiction in &amp;quot;obtaining or admission of non-existence&amp;quot;. If a piece of data is essential for a conclusion and yet does not exist then that non-existence provides bad faith on the part of the person reaching (and publishing) the conclusion.&lt;br /&gt;
&lt;br /&gt;
I do understand about 'public scrutiny'.  However this undefined  'public scrutiny' is vacuous testing 'in potentia'. I am suggesting actual public scrutiny. I am suggesting formulation of a hypothesis and a test which that hypothesis may fail. If it escapes refutation it will become corroborated. If it fails then we must accept that failure.&lt;br /&gt;
&lt;br /&gt;
Cheers&lt;br /&gt;
&lt;br /&gt;
Tony (on a windows mobile device and unable to &amp;quot;sign&amp;quot;)&lt;br /&gt;
&lt;br /&gt;
: The value in public scrutiny is to allow many to review the data.  Your insistence on a single &amp;quot;hypothesis&amp;quot; is contrary to the very benefit of public review.  Also, it's obvious to me that [[Lenski]] will not allow public scrutiny of the publicly funded data, and thus proposing a hypothesis would be a fool's errand.--[[User:Aschlafly|Aschlafly]] 16:01, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
Has the PNAS been contacted regarding this matter? --[[User:Jareddr|Jareddr]] 16:04, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
: You're welcome to do so.  PNAS does not make it easy to contact it, and accountability is far from clear at that publication.  If you can post an appropriate contact here, then I'd be happy to follow up with it about its stated policy and what the procedure is for ensuring compliance with it.--[[User:Aschlafly|Aschlafly]] 16:12, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::pnas@nas.edu • phone: 1-202-334-2679 • fax: 1-202-334-2739 {{unsigned|MarieB}}&lt;br /&gt;
&lt;br /&gt;
::: To elaborate on the contact info, &amp;quot;Authors must make Unique Materials (e.g., cloned DNAs; antibodies; bacterial, animal, or plant cells; viruses; and computer programs) promptly available on request by qualified researchers for their own use. Failure to comply will preclude future publication in the journal. It is reasonable for authors to charge a modest amount to cover the cost of preparing and shipping the requested material. Contact pnas@nas.edu if you have difficulty obtaining materials.&amp;quot; Here would be another good spot. [http://www.pnas.org/feedback]--[[User:Jareddr|Jareddr]] 16:32, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::: Thanks MarieB, I just called the number for PNAS that you provided.  The PNAS staffer said that I should first contact the author to request the data, which I have done, and if that is unsuccessful, as it has been, then the next step is to contact PNAS at the above email address.&lt;br /&gt;
&lt;br /&gt;
::: Jareddr's description of PNAS policy is incomplete.  In fact, PNAS has adopted &amp;quot;UPSIDE&amp;quot;, which is the Uniform Principle for Sharing Integral Data and Materials Expeditiously.  That standard establishes that the &amp;quot;author's obligation is ... to release data and materials to enable others to verify or replicate published findings,&amp;quot; and that the &amp;quot;upside&amp;quot; is that this &amp;quot;keeps science honest.&amp;quot;  Moreover, PNAS expressly rejects &amp;quot;a requirement that the material be used for research purposes.&amp;quot; [http://www.pnas.org/content/101/11/3721.full]--[[User:Aschlafly|Aschlafly]] 16:56, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::::Yeah but they really aren't saying that any tom, dick or harry should have access.  They say: &lt;br /&gt;
&lt;br /&gt;
::::&amp;quot;PNAS does not endorse this restriction because we believe that it would limit the sharing of materials with industry. Requiring a company to not make commercial use of scientific results seems wrong in principle and hardly enforceable. The overriding principle is that once something is published it should be freely shared by everyone.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
::::So they want the information to be freely shared with &amp;quot;industry&amp;quot;. [[User:MAnderson|MAnderson]] 17:34, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::::: The statement says &amp;quot;once something is published it should be freely shared '''by everyone'''.&amp;quot;  Do you really think a clarification is necessary about what &amp;quot;by everyone&amp;quot; means?--[[User:Aschlafly|Aschlafly]] 18:59, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
:::::: Andy in his letter Lenski did make it clear how his data would share '''by everyone'''. So long as '''everyone''' has a freezer capable of -80 degree temperatures, a contract of disposal of medical watse, the labratory to study the bacteria and are willing to sign the nessary paper work, then you can have it. This is because he is not going to go around handing out bacteria to people because it is not safe.&lt;br /&gt;
&lt;br /&gt;
:::::: All the papers listed above have the data you need. You seem to forget this was not one publication but many going back several years. The data for the early parts of the experiment are in the earlier papers, you just need to read them. The big problem of this saga is you don't know what data you actually want. [[User:DanielB|DanielB]] 19:17, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== What missing data? ==&lt;br /&gt;
&lt;br /&gt;
In order that this Conservapedia Challenge be run on a fair and comprehensible basis could someone provide a clear satatement of exactly what data is missing?  --[[User:DenningMR|DenningMR]] 18:07, 3 July 2008 (EDT)&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Talk:Conservapedia_challenge&amp;diff=486882</id>
		<title>Talk:Conservapedia challenge</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Talk:Conservapedia_challenge&amp;diff=486882"/>
		<updated>2008-07-03T23:17:33Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;A challenge! Very well, Sir, I accept!&lt;br /&gt;
&lt;br /&gt;
I am not a rich man and would be unable to handle all the data accumulated over twenty years. Neither do I think it acceptable to enjoin a publically funded organization to spend the large sums required to send such a large amount of data without a defined public benefit.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Let us, then, agree a hypothesis that can be tested by ' 'some' ', of Prof. Lenski's unpublished data.  I will then procure from said Professor either:&lt;br /&gt;
1) That very data, which I will then deliver to you, or&lt;br /&gt;
2) An admission from the Professor that he does not have that data&lt;br /&gt;
&lt;br /&gt;
If I succeed you will:&lt;br /&gt;
1) procure me one pint of Fuller's &amp;quot;London Pride&amp;quot; at the Nicholson's pub in the Strand, London, and display a picture of me drinking it on the front page of Conservapedia.&lt;br /&gt;
2) Publish a statement on the front page of Conservapedia stating that you accept Professor Lenski's honesty and professionalism.&lt;br /&gt;
&lt;br /&gt;
I await:&lt;br /&gt;
1) Your hypothesis&lt;br /&gt;
2) The data that would test it&lt;br /&gt;
3) Your &amp;quot;prize&amp;quot; should I fail&lt;br /&gt;
&lt;br /&gt;
Regards&lt;br /&gt;
Tony Lloyd (User:TonyLloyd&lt;br /&gt;
&lt;br /&gt;
: Your &amp;quot;offer&amp;quot; is fascinating but also self-contradictory.  On the one hand you imply that there are voluminous data (&amp;quot;spend the large sums required to send such a large amount of data&amp;quot;), but on the other hand you suggest that Lenski may not have any such data!  You also seem to misunderstand or ignore the purpose and benefits of public scrutiny, as the data are not merely for me (&amp;quot;your hypothesis&amp;quot; and &amp;quot;data that would test it&amp;quot;) but for all the public who paid for the data.--[[User:Aschlafly|Aschlafly]] 13:18, 3 July 2008 (EDT)&lt;br /&gt;
::As I have asked elsewhere Mr Schlafly I really do think you need to clarify [[Talk:Main_Page#Lenski.27s_data  | nature of the data requested and who would examine it]], and explain if you accept the [[Talk:Main_Page#Legal_means_to_get_Lenski.27s_data_2 | data are represented by the organisms]] (and if you think the data are not represented by the organisms explain why not.)--[[User:British_cons|British_cons]] [[User_talk:British_cons|(talk)]] 13:28, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
At least one blogger has already claimed to have won the challenge: [http://nolatitude.blogspot.com/2008/07/conservapedia-stubborn-idiocy-in-action.html No Latitude]. He cites and links to the following data:&lt;br /&gt;
http://myxo.css.msu.edu/lenski/pdf/2008,%20PNAS,%20Blount%20et%20al.pdf&lt;br /&gt;
http://www.pnas.org/content/103/24/9107.full.pdf+html&lt;br /&gt;
http://myxo.css.msu.edu/lenski/pdf/2004,%20Plant%20Breeding%20Reviews,%20Lenski.pdf&lt;br /&gt;
http://myxo.css.msu.edu/lenski/pdf/2003,%20JME,%20Lenski%20et%20al.pdf&lt;br /&gt;
http://myxo.css.msu.edu/lenski/pdf/2003,%20PNAS,%20Cooper%20et%20al.pdf&lt;br /&gt;
&lt;br /&gt;
Of these, the last is particularly data-rich.&lt;br /&gt;
&lt;br /&gt;
: The missing data are very specific.  The above citation list is a common tactic of distraction:  try to obscure by burying the reader with volumes of meaningless or less meaningful info.  Most of the dates on those cites are years ago, predating when key data could have even occurred.--[[User:Aschlafly|Aschlafly]] 14:05, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::''Most of the dates on those cites are years ago'' But not ALL of them, right? What about those citations which do not predate what you are looking for? Also, the Lenski dialogue now exists on several talk pages besides this one, some of them archived. I'm a busy person and do not have time to go hunting around through dozens if not hundreds of posts. Would it be too much of an imposition to ask you to state here, in a concise manner, what data exactly that would satisfy your request? - I say this in part because many of your interlocutors are trying to make YOU look unreasonable by making it appear as though you want Lenski to ship you on old mustard jar full of e coli (yes, I'm exaggerating)...I think it would do this discussion some good to refocus it on a short list of exactly what it is you're looking for...[[User:AliceBG|AliceBG]] 14:19, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::The oldest paper there is from generation 20,000.[[User:JPohl|JPohl]] 14:20, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
There is no contradiction in &amp;quot;obtaining or admission of non-existence&amp;quot;. If a piece of data is essential for a conclusion and yet does not exist then that non-existence provides bad faith on the part of the person reaching (and publishing) the conclusion.&lt;br /&gt;
&lt;br /&gt;
I do understand about 'public scrutiny'.  However this undefined  'public scrutiny' is vacuous testing 'in potentia'. I am suggesting actual public scrutiny. I am suggesting formulation of a hypothesis and a test which that hypothesis may fail. If it escapes refutation it will become corroborated. If it fails then we must accept that failure.&lt;br /&gt;
&lt;br /&gt;
Cheers&lt;br /&gt;
&lt;br /&gt;
Tony (on a windows mobile device and unable to &amp;quot;sign&amp;quot;)&lt;br /&gt;
&lt;br /&gt;
: The value in public scrutiny is to allow many to review the data.  Your insistence on a single &amp;quot;hypothesis&amp;quot; is contrary to the very benefit of public review.  Also, it's obvious to me that [[Lenski]] will not allow public scrutiny of the publicly funded data, and thus proposing a hypothesis would be a fool's errand.--[[User:Aschlafly|Aschlafly]] 16:01, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
Has the PNAS been contacted regarding this matter? --[[User:Jareddr|Jareddr]] 16:04, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
: You're welcome to do so.  PNAS does not make it easy to contact it, and accountability is far from clear at that publication.  If you can post an appropriate contact here, then I'd be happy to follow up with it about its stated policy and what the procedure is for ensuring compliance with it.--[[User:Aschlafly|Aschlafly]] 16:12, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::pnas@nas.edu • phone: 1-202-334-2679 • fax: 1-202-334-2739 {{unsigned|MarieB}}&lt;br /&gt;
&lt;br /&gt;
::: To elaborate on the contact info, &amp;quot;Authors must make Unique Materials (e.g., cloned DNAs; antibodies; bacterial, animal, or plant cells; viruses; and computer programs) promptly available on request by qualified researchers for their own use. Failure to comply will preclude future publication in the journal. It is reasonable for authors to charge a modest amount to cover the cost of preparing and shipping the requested material. Contact pnas@nas.edu if you have difficulty obtaining materials.&amp;quot; Here would be another good spot. [http://www.pnas.org/feedback]--[[User:Jareddr|Jareddr]] 16:32, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::: Thanks MarieB, I just called the number for PNAS that you provided.  The PNAS staffer said that I should first contact the author to request the data, which I have done, and if that is unsuccessful, as it has been, then the next step is to contact PNAS at the above email address.&lt;br /&gt;
&lt;br /&gt;
::: Jareddr's description of PNAS policy is incomplete.  In fact, PNAS has adopted &amp;quot;UPSIDE&amp;quot;, which is the Uniform Principle for Sharing Integral Data and Materials Expeditiously.  That standard establishes that the &amp;quot;author's obligation is ... to release data and materials to enable others to verify or replicate published findings,&amp;quot; and that the &amp;quot;upside&amp;quot; is that this &amp;quot;keeps science honest.&amp;quot;  Moreover, PNAS expressly rejects &amp;quot;a requirement that the material be used for research purposes.&amp;quot; [http://www.pnas.org/content/101/11/3721.full]--[[User:Aschlafly|Aschlafly]] 16:56, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::::Yeah but they really aren't saying that any tom, dick or harry should have access.  They say: &lt;br /&gt;
&lt;br /&gt;
::::&amp;quot;PNAS does not endorse this restriction because we believe that it would limit the sharing of materials with industry. Requiring a company to not make commercial use of scientific results seems wrong in principle and hardly enforceable. The overriding principle is that once something is published it should be freely shared by everyone.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
::::So they want the information to be freely shared with &amp;quot;industry&amp;quot;. [[User:MAnderson|MAnderson]] 17:34, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
::::: The statement says &amp;quot;once something is published it should be freely shared '''by everyone'''.&amp;quot;  Do you really think a clarification is necessary about what &amp;quot;by everyone&amp;quot; means?--[[User:Aschlafly|Aschlafly]] 18:59, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
:::::: Andy in his letter Lenski did make it clear how his data would share '''by everyone'''. So long as '''everyone''' has a freezer capable of -80 degree temperatures, a contract of disposal of medical watse, the labratory to study the bacteria and are willing to sign the nessary paper work, then you can have it. This is because he is not going to go around handing out bacteria to people because it is not safe.&lt;br /&gt;
&lt;br /&gt;
::::: All the papers listed above have the data you need. You seem to forget this was not one publication but many going back several years. The data for the early parts of the experiment are in the earlier papers, you just need to read them. The big problem of this saga is you don't know what data you actually want. [[User:DanielB|DanielB]] 19:17, 3 July 2008 (EDT)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== What missing data? ==&lt;br /&gt;
&lt;br /&gt;
In order that this Conservapedia Challenge be run on a fair and comprehensible basis could someone provide a clear satatement of exactly what data is missing?  --[[User:DenningMR|DenningMR]] 18:07, 3 July 2008 (EDT)&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486858</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486858"/>
		<updated>2008-07-03T22:52:20Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics hase devloped historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagorean theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486855</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486855"/>
		<updated>2008-07-03T22:51:30Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics hase devloped historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Trigonometry]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Similar triangles]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Pythagoras' theorem]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric funtion]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Right-angle trigonometry]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Trigonometric identities]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Hyperbolic trigonometric funtion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486847</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486847"/>
		<updated>2008-07-03T22:46:46Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics hase devloped historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Algebra===&lt;br /&gt;
&lt;br /&gt;
''Some comments on this one please''&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Set]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Group]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ordered Field]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ring]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Cartesian coordinants===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Cartesian coordinents]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Function plotting]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Conic section]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Surfaces]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===Linear equations===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Elementary algebra]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Linear equation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Systems of linear equation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486839</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486839"/>
		<updated>2008-07-03T22:39:31Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics hase devloped historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486837</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486837"/>
		<updated>2008-07-03T22:39:05Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Numbers */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics hase devloped historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Quaternion]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486833</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486833"/>
		<updated>2008-07-03T22:37:29Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics hase devloped historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[Category:Mathematics|*]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486831</id>
		<title>Conservapedia:Mathematics articles by development of concept</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Conservapedia:Mathematics_articles_by_development_of_concept&amp;diff=486831"/>
		<updated>2008-07-03T22:36:49Z</updated>

		<summary type="html">&lt;p&gt;DanielB: New page: {{cquote|God made the integers; all else is the work of man - Leopold Kronecker}}  __NOTOC__ Mathematics hase devloped historically as well as logically. This article lists mathematic ...&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{cquote|God made the integers; all else is the work of man - [[Leopold Kronecker]]}}&lt;br /&gt;
&lt;br /&gt;
__NOTOC__&lt;br /&gt;
Mathematics hase devloped historically as well as logically. This article lists mathematic articles by the either a logical devlopment or the historical means with which they were developed. It is not recommended you learn mathemtics this way as one subject will often involve ideas in another. It generally best to take a column approch to learning maths getting all the subjects at one level and then advancing, see :.&lt;br /&gt;
&lt;br /&gt;
This article is also to help editors better coordinate their efforts in writting articles&lt;br /&gt;
&lt;br /&gt;
===Differential calculus===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Tangent]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient (two points)|Slope]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Derivative]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Application of derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Partial derivatives]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Numbers]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Natural numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Integers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Rational number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Real numbers]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Complex number]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Gradient]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
===[[Series (mathematics)]]===&lt;br /&gt;
&lt;br /&gt;
{|style=&amp;quot;text-align:left&amp;quot; &lt;br /&gt;
|-valign=&amp;quot;top&amp;quot;&lt;br /&gt;
|[[Addition]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Summation]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Finite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Infinite series]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Taylor series]]&lt;br /&gt;
&lt;br /&gt;
[[Fourier series]]&lt;br /&gt;
&lt;br /&gt;
[[Reimann Zeta function]]&lt;br /&gt;
|&amp;lt;math&amp;gt;\rightarrow&amp;lt;/math&amp;gt;&lt;br /&gt;
|[[Ramanujan summation]]&lt;br /&gt;
|}&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=User:DanielB&amp;diff=486813</id>
		<title>User:DanielB</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=User:DanielB&amp;diff=486813"/>
		<updated>2008-07-03T22:15:40Z</updated>

		<summary type="html">&lt;p&gt;DanielB: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;{{QuoteBox2&lt;br /&gt;
|width=440&lt;br /&gt;
|align=center&lt;br /&gt;
|quote=Surely, God could have caused birds to fly with their bones made of solid gold, with their veins full of quicksilver, with their flesh heavier than lead, and with their wings exceedingly small. He did not, and that ought to show something. It is only in order to shield your ignorance that you put the Lord at every turn to the refuge of a miracle.&lt;br /&gt;
|source=[[Galileo Galilei]]&lt;br /&gt;
|}}&lt;br /&gt;
&lt;br /&gt;
----&lt;br /&gt;
'''My maths templates please improve they look awful'''&lt;br /&gt;
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{{math-e}}&lt;br /&gt;
{{math-m}}&lt;br /&gt;
{{math-h}}&lt;br /&gt;
{{math-a}}&lt;br /&gt;
&lt;br /&gt;
[[Conservapedia:Mathematics articles by development of concept]]&lt;br /&gt;
&lt;br /&gt;
[[Conservapedia:Mathematics articles by schooling level]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
	<entry>
		<id>https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486810</id>
		<title>Derivative (calculus)</title>
		<link rel="alternate" type="text/html" href="https://www.conservapedia.com/index.php?title=Derivative_(calculus)&amp;diff=486810"/>
		<updated>2008-07-03T22:14:20Z</updated>

		<summary type="html">&lt;p&gt;DanielB: /* Partial derivatives */ No need to keep adding concepts. That is what makes WP unreadable after while&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;In mathematics a '''derivative''' is the change in the function with respect to one of it vaiables. Essentially, the derivative is a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph.&lt;br /&gt;
&lt;br /&gt;
The process of finding a derivative is called '''differentiation'''.&lt;br /&gt;
&lt;br /&gt;
Algebraic differentiation is an important part of [[calculus]], an essential branch of [[mathematics]].&lt;br /&gt;
&lt;br /&gt;
For a single variable real function the derivative is the equation that given the [[gradient (two points)|slope]] of the line which is tangential at that point.&lt;br /&gt;
&lt;br /&gt;
When defined from the first principals, the derivative of a function is the limit of the average rate of change of the function over &amp;lt;math&amp;gt;[x,x+h]&amp;lt;/math&amp;gt; as &amp;lt;math&amp;gt;h&amp;lt;/math&amp;gt; tends to zero. In other words, the derivative&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;f'(x)=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
provided the above limit exists.&lt;br /&gt;
&lt;br /&gt;
Alternative notation also commonly found is &amp;lt;math&amp;gt;\frac{df}{dx}=f'(x)&amp;lt;/math&amp;gt;.&lt;br /&gt;
&lt;br /&gt;
For example, a polynomial can be differentiated by taking into account the linearity of the derivative, and by using the general formula:&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{d}{dx}(x^n) = nx^{(n-1)}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
(Proving this is a worth while exercise).&lt;br /&gt;
&lt;br /&gt;
For example, if &amp;lt;math&amp;gt;y = 3 x^2+2x&amp;lt;/math&amp;gt;, the derivative with respect to &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt; is &lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx} = 6 x+2&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
==Properties of the derivative==&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}(f(x)+g(x))=\frac{d}{dx}f(x)+\frac{d}{dx}g(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{d}{dx}cf(x)=c\frac{d}{dx}f(x)&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
*&amp;lt;math&amp;gt;\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&amp;lt;math&amp;gt;\frac{dy}{dx}&amp;lt;/math&amp;gt; is a proper quotient and a result,&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=f(x) \Leftrightarrow dy=f(x)dx&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
is a valid operation and is much used in solving [[differential equations]].&lt;br /&gt;
&lt;br /&gt;
The differential operator has an associated [[eigenfunction]],&lt;br /&gt;
&lt;br /&gt;
:&amp;lt;math&amp;gt;\frac{dy}{dx}=\lambda y\Leftrightarrow y=Ce^{\lambda x}&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
where [[e]] is the constant defined for this purpose.&lt;br /&gt;
&lt;br /&gt;
===Important differentiation rules===&lt;br /&gt;
*[[Product rule]]&lt;br /&gt;
*[[Quotient rule]]&lt;br /&gt;
*[[Chain rule]]&lt;br /&gt;
&lt;br /&gt;
The roots of differentiation are profoundly linked with tangency; ergo, this aspect of mathematics can first be perceived to have been developed during the time of the [[Ancient Greeks]] through the work of Greek geometers like [[Euclid]], [[Sanath]] and [[Archimides]].&lt;br /&gt;
&lt;br /&gt;
==See Also==&lt;br /&gt;
&lt;br /&gt;
[[Partial derivatives]]&lt;br /&gt;
&lt;br /&gt;
[[Category:Calculus]]&lt;br /&gt;
[[Category: Mathematics]]&lt;/div&gt;</summary>
		<author><name>DanielB</name></author>
	</entry>
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