Spring 2014

Email Address: blair ["at"] math.unm.edu

Course Web Page: http://www.math.unm.edu/~blair/math402s14.html

Office: SMLC 330

Office Hours: 3:30-5pm on Mondays and 10:15-11:45am on Tuesdays. Also by appointment.

**Text:** *Foundations of Analysis* by Joseph L. Taylor.

**Meeting times/location**: Tuesdays and Thursdays at 12:30-1:45pm in ~~Anthropology 178~~ Mitchell 208.

**Course Description** Uniform convergence of functions, infinite series, topology of R^n, continuous functions on R^n, differentiation in several variables including the inverse and implicit function theorems.

**Prerequisites** (from the catalog): Math 401/501.

Feb. 3: Note the room change! The class now meets in Mitchell 208, instead of the Anthropology building. Homework

Assignment #1--Due Thursday, January 30

3.4: 1,3,5,10

6.1: 2-9

Reading: 3.4, 6.1, 6.2

Not collected: 3.4: 2,4; 6.1: 12

Assignment #2--Due Tuesday, February 4

See handout

Assignment #3--Due Tuesday, February 11

6.3: 5,6,11

6.4: 1,3,6,9,10

Reading: 6.3, 6.4

Not collected: 6.3: 1-4,7; 6.4: 4,5,7,8

Notes: For 6.4 #6, you can use the trick from class where you take logarithms in order to compute the radius of convergence. For 6.4 #8 (not collected), it is a bit of a trick question, the answer is NOT 2! For 6.4 #9, you may use the usual facts about the derivative of the inverse tangent function from calculus.

Assignment #4--Due Thursday, February 27

See handout

Assignment #5--Due Tuesday, March 4

7.2: 6,8

7.3: 1,2,3,7(a),9

Reading: 7.3, 7.4

Not collected: 7.2: 1-5,7,10,12; 7.3: 4,6,14

Notes: The problem 7.3 #7(a) means prove only part (a) of Theorem 7.3.7. For the not collected problem 7.2 #10, you can use #6 and #8 from the same section to get a short proof.

Assignment #6--Due Thursday, March 13

See handout

Assignment #7--Due Tuesday, April 1

8.1: 3,6,8,10

8.2: 1(a,b,c,e),4,10,11

Reading: 8.1, 8.2, 8.3

Not collected: 8.1: 1,5,9; 8.2: 5,6

Assignment #8--Due Tuesday, April 15

8.4: 13, 15, 16

9.1: 1, 7, 8, 9, 10

Reading: 8.4, 8.5, 9.1, 9.2

Not collected: 8.4: 1-10, 14 8.5: 1-5 9.1: 1-4, 6

Notes: In 9.2 #8, your solution should address the values of p for which the partial derivative in x does not exist.

Assignment #9--Due Tuesday, April 22

See handout

Assignment #10--Due Tuesday, April 29

9.4: 2,8,9,10

9.5: 2,3,6,7

Reading: 9.4, 9.5, 9.6

Not collected: 9.4: 1,3,4,6,11,14; 9.5: 1,8,9

Assignment #11--Due Tuesday, May 6

9.5: 9,12

9.6: 2,3,4,7,10

Reading: 9.5, 9.6, 9.7

Not collected: 9.5: 8; 9.6: 1

Notes: For 9.6 #3, answer the first question regarding existence of a smooth local inverse, but not the second question on differential of the inverse.