Calculus III
Course notes for Fall 2003
2003 final exam and old exams from 2001, 2000, and 1999
Maple worksheets illustrating things in class and
on the homework for Fall 2003
A collection of Maple worksheets
Maple is a computer package that lets you graph functions of one or two
variables, do symbolic algebra and calculus, and many other things. Some
useful links:
The worksheets below are intended to get you started working with Maple.
They come in two versions; one is a web page, the other is a Maple worksheet
which you can download and work with using Maple. Downloading a worksheet
is pretty easy with a PC; you just click on the link to the worksheet and
your browser should download the file and launch Maple. On a Macintosh
you can press Control at the same time as you click, then Save this Link
as, then tell the browser to save it to the desktop. Then launch
Maple yourself, by clicking on the Apple at the upper left of the screen,
then Applications, then Maple. From Maple, use File, Open, and get
to, say, the desktop to open the worksheet. As soon as you save it,
the Macintosh with recognize the file as a Maple worksheet. From
then on, double clicking on the file icon will launch Maple.
Note that the Maple output has been removed from the worksheets.
This way you can see how Maple operates. Click in the first red command
in the worksheet and hit enter to tell Maple to process it. On the
other hand, the output has been left in in the web pages.
Maple basics
Calculus II with Maple

Maple can be a big help with techniques of integration. See the worksheet
integration.mws
or the web page.

It's easy to visualize Taylor series for functions. To see the Taylor
series for cosine, download the worksheet taylor_cosine.mws
or see the web page.
Multivariate Calculus

Maple lets you do things with vectors, although in my opinion it is clumsy.
See the worksheet vectors.mws vectors.mws
or the web page.

Maple lets you plot vector valued functions too. See the worksheet
vectorvalued.mws
or the web page.

In Maple 7, it seems that you have to deal with vectorvalued functions
differently than with previous versions. I still have not found out
how to define, add, and differentiate vector valued functions the way I
want to. You can see the worksheet vectorvalued7.mws,
or the web page.

One of the very best things about Maple is that it can make threedimensional
plots, and then you can rotate the figure to see it from different angles.
You can do this if you download the worksheet surfaceplots.mws,
but not if you just look at the web page.

One of the best kinds of functions of two variables to understand are the
paraboloids. You can download the worksheet paraboloids.mws
or view the web page.

For multiple integrals, it is very helpful to be able to visualize the
threedimensional solid whose volume you are computing. the worksheet
multiple_int.mws
is highly recommended because you can click and rotate the graphs, or you
can just look at the
web page.