Math 2433 (Calculus III)

Fall 2004

Instructor:

John Albert
Office: PHSC 1004, Ext. 5-3782.
Office hours: Mon, 10:30 AM; Wed and Thurs, 2:30-3:30 PM (or by appointment)
E-mail: jalbert@ou.edu

Announcements

Homework

Assignment

Due Date

Problems
1 Monday, Aug. 30 11.1 #5, 10, 12; 11.2 #1, 12, 13, 18, 25, 31, 34
2 Friday, Sept. 10 11.2 #41, 48; 11.3 #17, 20, 25, 55; 11.4 #10, 12, 18, 21
3 Friday, Sept. 17 11.4 #27, 29, 45, 46
4 Wednesday, Sept. 22 11.5 #28, 29, 30; 11.6 #9, 10, 12
5 Friday, Oct. 1 12.2 #11, 12, 14, 19, 21; 12.3 #3, 4, 15, 21, 25
6 Monday, Oct. 11 12.4 #7, 8, 10, 23, 38; 12.5 #8, 11; 12.6 #5, 6, 7
7 Wed, Oct. 20 12.8 #4, 5, 7, 8, 9; 12.9 #4, 18; 12.10 #3, 4, 9
8 Fri, Nov. 5 13.1 #2, 6, 7, 10, 11, 13, 15; 13.2 #11, 13, 19, 25
9 Fri, Nov. 12 13.3 #1, 3, 15, 17, 21, 23, 51; 13.4 #3, 15, 25, 41
10 Fri, Nov. 19 13.5 #7, 10, 12, 23, 26, 28, 30, 33, 51, 59
11 Wed, Dec. 1 13.6 #3, 8, 13, 35; 13.7 #4, 11, 17, 19, 40, 42
12 Mon, Dec. 6 14.2 #2, 3, 5, 9, 10, 17, 19, 23, 31, 32

Quiz dates

Exam dates

Links

Cycloids and other curves

In the early middle ages, little mathematics was done beyond what the ancient Greeks had discovered a millenium earlier. Eventually, however, the discipline of mathematics awoke again, and the frontiers of mathematical knowledge were pushed beyond the explorations of the Greeks. Many of the first advances over classical Greek mathematics had to do with the cycloid, the curve traced out by a point on the rim of a rolling wheel. In attempting to answer questions about the cycloid, mathematicians were led to ideas that eventually were systematized into what is today known as calculus. Some of these questions were: What is the area under one arch of the cycloid? How long is one arch of the cycloid? How much volume would be generated by revolving the area under one arch of the cycloid around the axis which forms its base? These were extremely difficult problems for Renaissance mathematicians, and formed the basis of numerous challenges they posed to each other. You, on the other hand, having had a year or so of modern calculus, should be able to solve them fairly easily.

For more about cycloids and their history, see the entry on cycloids on the St. Andrews' "Famous Curves" website, or this web page from Zimbabwe.

The problems about cycloids mentioned above were actually solved before the invention of calculus. In fact, all the methods you learn for solving problems in calculus class had already been anticipated by mathematicians in the years just before calculus was invented. When we talk about the "invention of calculus", what we really mean is a systematization and unification of what had previously been a bunch of seemingly unrelated problem-solving techniques. For example, the techniques you use as calculus students to solve problems about cycloids can be used with very little change to solve problems about an endless variety of other interesting curves. For discussions of a few of these other curves, see the Famous Curves website.