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→exact (differential) equation: new section
[http://conservapedia.com/index.php?title=Talk:Biblical_scientific_foreknowledge&diff=prev&oldid=793340 We don't point out people's spelling errors on talk pages]. Thank you. And sorry again for earlier today. [[User:JonG|~]] [[User_talk:JonG|JonG]] [[Special:Contributions/JonG|~]] 15:14, 9 July 2010 (EDT)
[http://conservapedia.com/index.php?title=Talk:Biblical_scientific_foreknowledge&diff=prev&oldid=793340 We don't point out people's spelling errors on talk pages]. Thank you. And sorry again for earlier today. [[User:JonG|~]] [[User_talk:JonG|JonG]] [[Special:Contributions/JonG|~]] 15:14, 9 July 2010 (EDT)
:I can point out spelling errors wherever I please. :P [[User:PhyllisS|PhyllisS]] 22:50, 9 July 2010 (EDT)
:I can point out spelling errors wherever I please. :P [[User:PhyllisS|PhyllisS]] 22:50, 9 July 2010 (EDT)
== exact (differential) equation ==
While looking through recent mathematical changes (a hobby of mine) I came across your [[exact equation]] article. I have a few comments on improving it.
The first thing that caught my attention was the title. "Exact equation"? Aren't all equations exact? This is mathematics, after all! The problem is that "exact" has a very specialized meaning in this context. I would suggest renaming the page to "exact differential equation".
'''You need to motivate this with an example!!!''' And you need to say something like
"The solution is φ = constant, where φ is determined by integrating M and N." I believe the integration is something like
:<math>\phi(t, y) = \int_0^t M(s, 0) ds + \int_0^y N(t, s) ds</math>
but I'm not sure I have it right. Please check that.
Go through the example to find φ by integrating, then check that
:<math>\frac{\partial \phi}{\partial t} = M</math>
and
:<math>\frac{\partial \phi}{\partial y} = N</math>
and that any function φ = some constant, when turned into the corresponding dy/dt, satisfies the original equation. Be sure to emphasize that one must check first that
:<math>\frac{\partial M}{\partial y} = \frac{\partial N}{\partial t}</math>
(That's the condition for "exactness" of the differential form M dt + N dy.)
And take out phrases like "only write once in the combined expression" and "plug into the quadratic formula" unless you give examples of the combined expression and the quadratic equation that arises.
Finally, you can make equations look like big-as-life equations by putting a "\," at the end, just before the closing <nowiki></math></nowiki>. See [[Tips_for_writing_math_and_science_articles]] for more info.
, [[User:SamHB|SamHB]] 09:33, 29 July 2010 (EDT)