# Cal III (Resource page)

## Homework Assignments and Practice Tests

These assignments act as "practice tests" for the class tests and exam - in addition to being homework.
After they are due I will post the answers on the course webpage Please let me know if you find any errors.

Problems?

Assignments

Assignment 3 (PDF Format)   (PS format)

Assignment 4 (PDF Format)   (PS format)

Assignment 4 1/2 (PDF Format)   (PS format)

Assignment 5 (PDF Format)   (PS format)

# Cal III notes

(Some of these notes are taken from your text book or past texts.)

Review: Notes on topics from Cal II

A recommendation from Ivo: here's a quite nice, free, graphing web app that you can use to plot polar and parametric graphs (and even, with a bit of experimentation, 3D graphs). Try it out (a tip: try their examples, and just alter the equations and parameters to get other graphs you want; experiment to your heart's - or should that be "cardioid's"? - content!).
Desmos.com Features page
Polar graphs
Parametric graphs

Some curves in polar coordinates.  Some standard curves and the equations that generate them.
Polar Graph paper (6 graphs per page)

Maple worksheet: Introduction to polar coordinates.  On my Links page, I give some links to sites with Maple tutorials and exercises in Cal I, II, III - here is a sample of a Maple file you can open in Maple and experiment on, taken from that site. (Don't try to read this in your browser! Right click, save link/target as ..., and then open the file with Maple.)
Please don't print this out at the college - the idea is for you to read and experiment with this file in Maple, not to print it and read it off-screen. It's long enough for lab technicians to worry about the cost of printing!

If you want a copy of this tutorial: Here is a PDF printout of the text and graphs - you might find it good reading, and the graphs are very pretty! (This you can print out!! Though there are some errors, as explained at the start of the document, in the printed version. Eg, Limaçon is missing its ç!)

Summary notes on vector geometry (by Denis Sevee)

Quadric surfaces.  Some standard surfaces and the equations that generate them.

The quadrics discussed in class: (New: Images updated in March 2015)

Some worksheets exploring extra topics
(Some of these have been possible CAM assignments in some years)
Aspects of Pi (PDF format)     (Uses Chp 8, Stewart, Essential Calculus)
Calculating ζ(2) several ways     (A variant of "Aspects of Pi" - Uses Chp 8 and 12)
Some properties of the (inverted) cycloid (PDF format)     (Uses Chp 9)

Video showing a cycloid is a tautochrone (Slow Motion)
[Regular speed version]   [AVI version]   (These are larger files than the slowmo version; you might want to download them to your computer ("left click ...") and view them off-line.)

Do curve balls really curve? (PDF format)     (Uses Chp 10)
Envelopes (PDF format)     (Uses Chp 11)
The 2nd derivative test and the chain rule (Assignment 4 1/2) (PDF Format)   (PS format)     (Uses Chp 11)
The Tower of Babel and other stories     (Uses Chps 10-12)

And more:
Bill Boshuck's notes on derivatives of multivariable functions     (Chp 11)

Off-campus notes:
Paul's Online Math Notes (Notes for Cal I, Cal II and Cal III - but note that his courses are not exactly the same as ours, so some topics may be missing, extra, or located in another course)

FLATLAND - A Romance of many dimensions
A novel dealing with the question of whether the fourth dimension can exist, and how we might seek to perceive it (based on the analogy of a 2D being trying to imagine a 3D world). Lots of fun, even if it was written long ago.
If you want this in ebook format, try this (epub); other formats here.

Another helpful page in visualizing 4D
[This Union College teacher's Home Page has a lot of good stuff on it. Including tips for studying, mathematical art, movies for maths (including one on hyperboloids, as well as the 4D stuff), geometry and web math projects, and advice for life.]