# Math 401, Advanced Calculus Spring 2011

## General Information

Instructor: Matthew Blair
Course Web Page: http://www.math.unm.edu/~blair/math401.html
Office: SMLC 330
Office Hours: Tuesdays 2-4pm, and by appointment.

Text: Analysis: With an Introduction to Proof, Fourth Edition, by Steven R. Lay.

Meeting times/location: Tuesdays and Thursdays at 12:30-1:45pm in SMLC 356.
Recitation: Wednesdays at 12-12:50pm in SMLC 356.
Recitation leader: Jean Carlo Moraes (jmoraes ["at"] math.unm.edu)

Course Syllabus (in .pdf format)

Announcements

February 8: Problem 12.13 has been moved from Assignment #3 to Assignment #4. Hand this problem in on the 17th.

February 10: Assignment #4 has been redone to meet the pace of the class. It will not have problems from section 14 on it.

Homework

Assignment #1--Due Thursday, January 27

Exercises: 2.3, 2.6(c,d), 3.6(a,c,f,i), 3.7(a,b,c,g), 3.8, 4.3, 4.4, 4.10, 4.11, 4.16, 5.7, 5.10, 5.11, 5.19, 5.20, 5.25, 6.10, 6.11(a,b,c,h), 6.14

Assignment #2--Due Thursday, February 3

Exercises: 7.6, 7.7(a,b,e,f), 7.9, 7.12, 7.15, 7.26, 7.27, 7.29, 8.3, 8.4, 8.7, 8.10, 8.11

Assignment #3--Due Thursday, February 10

Exercises: 10.3, 10.7, 10.21(b,c), 10.25, 11.3(a,b,i,j,k,l,m), 11.4, 11.6, 11.7, 12.6, 12.7, 12.9, 12.13

Assignment #4--Due Thursday, February 17

Exercises: 12.12(a,b), 12.13, 13.3(a,b), 13.5(b,c), 13.12, 13.14, 13.15, 14.3(a,c), 14.4, 14.5, 14.8

Assignment #5--Due Thursday, February 24

Exercises: 14.3(a,b,c), 14.4, 14.5, 14.8, 14.12

Assignment #6--Due Thursday, March 10

Exercises: 16.7(f), 16.8(a,b), 16.11, 16.12, 16.15, 16.16(a), 17.3, 17.5(b,f), 17.6(c,d), 17.15(c), 17.17
Reading: Sections 16, 17, 18, 19
Notes: For 16.7(f), use Bernoulli's inequality (exercise 10.22) as suggested by the hint in the back. While the inequality is not difficult to prove, you can take it for granted here. For 17.15(c), don't hesitate to first try 17.15(a) as a "warm up" for this exercise, even though part (a) is not assigned. Going through that exercise and considering the hint will be helpful.

Assignment #7--Due Thursday, March 24

Exercises: 18.3(a,e), 18.7, 18.13, 18.15, 19.4(a,b), 19.6(b), 19.9, 19.10, 19.17
Reading: Sections 18, 19, 20, 21

Assignment #8--Due Thursday, March 31

Exercises: 20.6(b), 20.17, 20.18, 21.4, 21.6(e), 21.10, 21.13, 21.16, 21.18
Notes: Exercise 20.17 will be slightly easier once you've gone through Section 21 thoroughly. On your own (meaning you do not need to address this in your write up), note the connection between this problem and Exercise 21.5. Also, on your own, note the connection between Exercise 21.13 and Exercise 20.16.

Assignment #9--Due Thursday, April 7

Exercises: 22.5, 22.7, 22.11, 22.13, 23.3(a,b), 23.4(b), 23.8, 23.11

Assignment #10--Due Thursday, April 21

Exercises: 25.3, 25.4(c,d), 25.6, 25.17(a,b,c), 26.8, 26.11, 26.15, 26.17, 27.4(c,e,f), 27.6

Assignment #11--Due Thursday, April 28

Exercises: 27.11, 28.4, 28.5, 28.10, 28.11, 29.6, 29.8, 29.13, 29.16

Assignment #12--Due Wednesday, May 4

Exercises: 30.6, 30.7, 30.9, 30.14, 30.15, 30.20, 31.8
Notes: For exercise 30.6, you may want to consider proving the contrapositive.

Assignment #13--Not collected

Exercises: 31.5, 31.9, 31.11, 31.14, 31.17(a,c,e)