Math 402, Advanced Calculus II
Spring 2012

General Information

Instructor: Matthew Blair
Email Address: blair ["at"] math.unm.edu
Office: SMLC 330
Office Hours: Wednesdays 2:30-4:30pm, or by appointment.
Course Web Page: http://www.math.unm.edu/~blair/math402.html

Text: Introduction to Analysis, 4th Edition, by William R. Wade.

Meeting times/location: MWF at 12:00-12:50pm in SMLC 356.

Course Description (from the catalog): Generalization of 401/501 to several variables and metric spaces: sequences, limits, compactness and continuity on metric spaces; interchange of limit operations; series, power series; partial derivatives; fixed point, implicit and inverse function theorems; multiple integrals.

Course Syllabus (in .pdf format)

Exam dates (all are Fridays): February 17, March 30, and May 4 (last day of class)

Announcements

Homework

Assignment #1--Due Friday, January 27

Exercises: 5.1.2(b), 5.1.3, 5.1.4, 5.1.8, 5.1.10
Reading: 5.1, 5.2
Not collected: 5.1.2(a,c), 5.1.5, 5.1.6, 5.1.9

Assignment #2--Due Friday, February 3

Exercises: 5.2.5, 5.2.6, 5.2.8, 5.2.10
Reading: 5.2, 5.3
Not collected: 5.2.2, 5.2.9

Assignment #3--Due Friday, February 10

Exercises: 5.3.3, 5.3.7(a,b,c), 5.4.2(a), 6.1.3(a,c), 6.1.6
Reading: 6.1, 6.2, Elementary improper integrals
Not collected: 5.3.1, 5.3.2, 5.3.4, 5.3.5, 5.4.2(b), 6.1.1, 6.1.4, 6.1.5

Assignment #4--Due Friday, February 17

Exercises: 6.2.6, 6.3.4, 6.3.7
Reading: 6.3, 6.4
Not collected: 6.2.2, 6.2.3, 6.2.5, 6.2.7, 6.3.1, 6.3.2, 6.4.1, 6.4.2, 6.4.4

Assignment #5--Due Friday, February 24

Exercises: 7.1.1, 7.1.2(b), 7.1.3, 7.1.5(b,c,d)
Reading: 7.1, 7.2
Not collected: 7.1.5(a), 7.1.7, 7.1.9

Assignment #6--Due Friday, March 2

Exercises: 7.2.5, 7.3.3, 7.3.5, 7.3.6
Reading: 7.2, 7.3
Not collected: 6.1.2(a), 7.2.1, 7.2.2, 7.2.3, 7.3.1, 7.3.2, 7.3.7
Notes: Exercise 6.1.2(a) will be a helpful preliminary exercise for 7.2.5

Assignment #7--Not collected

Reading: 7.2, 7.3
Not collected: 8.1.9, 8.1.10, 8.2.4, 8.2.5, 8.2.10, 8.2.11


Assignment #8--Due March 23

Exercises: 10.1.3(a,b), 10.1.8, 10.1.9, 10.2.3
Reading: 10.1, 10.2, 10.3
Not collected: 10.1.3(c), 10.1.4, 10.1.5, 10.1.6, 10.2.1


Assignment #9--Due April 6

Exercises: 10.3.5, 10.3.7(a,b), 10.4.1(a,c), 10.4.3, 10.4.8
Reading: 10.3, 10.4, 10.5
Not collected: 10.3.1, 10.3.4, 10.3.8, 10.4.1(b,d), 10.4.2, 10.4.7
Note: On problem 10.4.1(a), use the definition of compactness to show that the set is compact.

Assignment #10--Due April 13

Exercises: 10.5.5, 10.5.8, 10.6.5, 10.6.8
Reading: 10.5, 10.6, 11.1
Not collected: 10.5.6, 10.6.3, 10.6.6, 10.6.7

Assignment #11--Due April 20

Exercises: 11.1.3, 11.1.5, 11.2.3, 11.2.6, 11.2.7, 11.2.8
Reading: 11.1, 11.2, 11.3
Not collected: 11.1.5, 11.2.4, 11.2.5, 11.2.9
Note: Exercises 11.2.3, 11.2.6, 11.2.7 will require you to use "strategy 3" at the bottom of p. 399.

Assignment #12--Due April 27

Exercises: 11.3.6(a,b,c,d), 11.4.2(a), 11.4.3, 11.4.6, 11.4.8
Reading: 11.3, 11.4, 11.5
Not collected: 11.3.2, 11.3.3, 11.3.5, 11.3.6e, 11.4.4, 11.4.5, 11.4.9


Assignment #13--Not collected, review for the final

Exercises: 11.5.1, 11.5.4, 11.5.6, 11.5.8, 11.6.1, 11.6.2, 11.6.3, 11.6.4, 11.6.6
Reading: 11.5, 11.6
Note: On Exercise 11.6.6(a), you can solve for y in terms of s,t by using substitution to obtain the quadratic y^2-sy+t=0. Plugging this back into the equation for s, this gives you an expression for x in terms of s,t.