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→Vectors, and Vector Functions
Vectors are the bread and butter of multivariable calculus because they pack multiple variables into a single, easily manipulated quantity. Let's look at some more specific examples.
Vectors are the bread and butter of multivariable calculus because they pack multiple variables into a single, easily manipulated quantity. Let's look at some more specific examples.
In our first descriptions, we used a coordinate system you should be familiar with call "polar coordinates." If you aren't familiar with this system, we will review them shortly. When using Cartesian coordinates, vectors are very, very familiar. The point <math>(x,y) \ </math> has position vector, or put more simply, ''is'' the vector written <math>\begin{pmatrix}x\\y\end{pmatrix} \ </math>
In our first descriptions, we used a coordinate system you should be familiar with call "polar coordinates." If you aren't familiar with this system, we will review them shortly. When using Cartesian coordinates, vectors are very, very familiar. The point <math>(x,y) \ </math> has position vector, or put more simply, ''is'' the vector written <math>\begin{pmatrix}x\\y\end{pmatrix} \ </math>. See illustration at right. Unlike variables which may be numbers, like <math>a, x, \ </math> etc., vectors are usually written <math>\vec{v} \ </math> or <math>\mathbf{v} \ </math>. While the latter is common in print and online, we will use the former since it is more easily duplicated in handwriting.
In three dimensional space we use three variables to write down a vector. In Cartesian coordinates, this would look like <math>\vec{v} = \begin{pmatrix}x\\y\\z\end{pmatrix} \ </math>.
=Coordinate Systems=
=Coordinate Systems=