Math 2934 (Calculus III)

Fall 2015

Red mulberry (Morus rubra). You'll find lots of mulberry trees growing wild in rural Norman. The fruits are edible. In fact, some people think they are delicious. Image taken from the Withlacoochee Permaculture Guild website.

Instructor:

John Albert

Office: PHSC 1004, Ext. 5-3782.

Office hours: Mon, Wed, Thurs 2:30 to 3:30 pm, or by appointment

E-mail: jalbert@ou.edu

Announcements

Homework

Assignment

Due Date

Problems

1 Thursday, Sept. 3 12.2 #15, 17, 21, 23; 12.3 #15, 24, 25, 39; 12.4 #1, 3.

2 Thursday, Sept. 10 12.4 #30, 35; 12.5 #7, 10, 13, 21, 29, 31, 34, 48.

3 Thursday, Sept. 17 12.6 #11, 12, 24, 41, 44; 13.2 #4, 13, 19, 24, 27.

4 Thursday, Sept. 24 13.3 #1, 2; 13.4 #9, 10, 11; 14.1 #52; 14.3 #3(a,b), 5, 16.

5 Thursday, Oct. 1 14.3 #11, 32, 34, 35, 48, 50, 61; 14.4 #1, 4.

6 Thursday, Oct. 8 14.5 #27, 28, 32, 33, 35; 14.6 #9, 12, 21, 43, 44.

7 Thursday, Oct. 15 14.4 #31, 34; 14.6 #56; 14.7 #6, 12, 43, 44, 48, 51.

8 Thursday, Oct. 22 15.1 #1(a), 12; 15.2 #5, 7, 8, 11, 26, 28; 15.3 #8, 9.

9 Thursday, Oct. 29 15.4 #11, 19, 27.

10 Friday, Nov. 6 15.6 #6, 8; 15.7 #6, 8, 13, 33, 39.

11 Friday, Nov. 13 15.8 #20, 21; 15.9 #23, 30; 16.2 #14, 15, 16, 19, 20, 21.

12 Friday, Nov. 20 16.3 #13, 16, 18, 19, 30; 16.4 #2.

13 Tuesday, Dec. 8 16.4 #4, 5, 13, 22; 16.5 #2, 3, 27; 16.7 #23, 24, 26.

Quiz dates

Quiz 1: Friday, Sept. 11 (Assts. 1, 2)

Quiz 2: Friday, Sept. 18 (Asst. 3)

Quiz 3: Wednesday, Oct. 7 (Assts. 4 and 5, sections 14.3 and 14.4 only)

Quiz 4: Friday, Oct. 23 (Assts. 6 and 7)

Quiz 5: Friday, Nov. 13 (Assts. 8, 9, 10)

Quiz 6: Tuesday, Dec. 1 (Assts. 11, 12)

Quiz 7: Thursday, Dec. 9 (Asst. 13)

Exam dates

Exam 1: Friday, Sept. 25 (Assts. 1, 2, 3)

Exam 2: Friday, Oct. 30 (Assts. 4, 5, 6, 7, 8)

Exam 3: Friday, Dec. 4

Final Exam: Monday Dec. 14 from 8:00 am to 1:00 am, in PHSC 102.

Links

I mentioned in class that the method of evaluating an "impossible to evaluate" integral by switching the order of integration is a kind of magic. Another quasi-magical method for evaluating integrals is the trick of "differentiating under the integral", as practiced by Richard Feynman, the Nobel-prize-winning physicist. Here is a nice write-up showing how to use the trick on some examples: Integration: The Feynman Way.
We were wondering in class about possible formulas for the volumes of prism-shaped objects. One relevant formula goes by the name of the "prismoidal formula", and states that the volumes of some objects can be computed by the formula V = (1/6)(B + 4M + T), where B is the area of the base, M is the area of the midsection, and T is the area of the top. Somewhat surprisingly, this formula works not only for prism-shaped objects, but also for objects such as spheres and ellipsoids. Can you see why it is true for a sphere? A discussion of this formula is given in the article Some Notes on The Prismoidal Formula, by B. E. Meserve and R. E. Pingry, Mathematics Teacher, Vol. 45, No. 4, April 1952, pp. 257-263.
As I mentioned in class, our textbook notes that whenever you take the cross product of two vectors a and b, it "turns out" that the direction of the resulting vector axb is determined by the right-hand rule: if you curl the fingers of your right hand in the direction from a to b, then your thumb points in the direction of axb. But how would one prove this? An explanation (due to Fuchang Gao at the University of Idaho in beautiful Moscow, Idaho) can be found here.

Assignment	Due Date	Problems
1	Thursday, Sept. 3	12.2 #15, 17, 21, 23; 12.3 #15, 24, 25, 39; 12.4 #1, 3.
2	Thursday, Sept. 10	12.4 #30, 35; 12.5 #7, 10, 13, 21, 29, 31, 34, 48.
3	Thursday, Sept. 17	12.6 #11, 12, 24, 41, 44; 13.2 #4, 13, 19, 24, 27.
4	Thursday, Sept. 24	13.3 #1, 2; 13.4 #9, 10, 11; 14.1 #52; 14.3 #3(a,b), 5, 16.
5	Thursday, Oct. 1	14.3 #11, 32, 34, 35, 48, 50, 61; 14.4 #1, 4.
6	Thursday, Oct. 8	14.5 #27, 28, 32, 33, 35; 14.6 #9, 12, 21, 43, 44.
7	Thursday, Oct. 15	14.4 #31, 34; 14.6 #56; 14.7 #6, 12, 43, 44, 48, 51.
8	Thursday, Oct. 22	15.1 #1(a), 12; 15.2 #5, 7, 8, 11, 26, 28; 15.3 #8, 9.
9	Thursday, Oct. 29	15.4 #11, 19, 27.
10	Friday, Nov. 6	15.6 #6, 8; 15.7 #6, 8, 13, 33, 39.
11	Friday, Nov. 13	15.8 #20, 21; 15.9 #23, 30; 16.2 #14, 15, 16, 19, 20, 21.
12	Friday, Nov. 20	16.3 #13, 16, 18, 19, 30; 16.4 #2.
13	Tuesday, Dec. 8	16.4 #4, 5, 13, 22; 16.5 #2, 3, 27; 16.7 #23, 24, 26.