Vector Calculus Web Page by Kris
What will I find here?
This web site is designed to provide a supplement to any course on vector
calculus. It includes examples, a throrough coverage of all the techniques,
and terminology that appears in studying functions of several variables.
Also included are a few sections of review material, in case you don't
remember how to graph functions of one variable, or integrate, or
differentiate. There are also projects (and solutions) which cover a single
topic in as much detail as we felt necessary. The actual material of the
web site is grouped by topic, rather than in the standard textbook format.
The appendix has a link to illustrate the relationship between the topics
here and the consortium text used here at the University of Arizona.
Why did you create this page?
As a graduate teaching assistant, I have taught vector calculus
several times. No matter what textbook is used, I feel that there will
always be gaps in the material covered. I wanted to create a website that
would fill in some of these gaps at no cost to the student (other than time,
of course.) Teaching has taught me that there is never enough time for even
the best lecturer to do justice to every important topic. I hope that the
material here will be valuable to students as well as instructors for
deciding both how to organize the material in their heads as well as what is
really important.
How do I use this web site?
At the bottom of this page, you'll find a link to the main page of the site.
It's that page that you should bookmark, since all of the links to the various
topics are there. Links to other web sites can be accessed through this
page, as well as reference material that might be worth looking at. Once you
pass into a topic (say, Line Integrals) you will find yourself in a self-
contained table of contents that will let you flip through various sections
of the topic. To get back to the main page, simply return to the table of
contents for that section and you'll find a link. Happy hunting!
Why multivariable calculus?
There are many quantities that can be described by a single number. If you
speak of temperature, mass, length, time, and so forth, a single quantity
can fully express the details. A single number like this is called a
scalar. A variable (such as t, x, u or v) that holds a single
value is a scalar variable. A function that takes in different
quantities and outputs a single number is called a scalar function
or a scalar field. First and second semester calculus deals with
derivatives (rates of change) and integrals (areas under the curve) of
scalar fields.
Unfortunately, scalars can't be used for everything. For example, the
position of an object in space is described by three numbers. Quantities
that keep track of several things at the same time (sort of a list) are
called vectors. A vector field or vector-valued
function takes in vector quantities and spits out vectors. Since many
quantities in nature are vectors (electric fields, velocity fields of
fluids) we must have tools for dealing with rates of changes and so forth
of vector quantities.
Please be patient, the site is still in its early stages. Much work is
still undone.
Copyright © 1998 by Kris H. Green
The Vector Calculus Website at
http://www.math.arizona.edu/~vector
Last update, May 8, 1998.