Math 401, Advanced Calculus
Spring 2011
General Information
Instructor: Matthew Blair
Email Address: blair ["at"] math.unm.edu
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
Reading: Sections 1-7
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
Reading: Sections 7,8,10,11
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
Reading: Sections 10,11,12,13
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
Reading: Sections 13, 14, 16
Assignment #5--Due Thursday, February 24
Exercises: 14.3(a,b,c), 14.4, 14.5, 14.8, 14.12
Reading: Sections 14, 16
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
Reading: Sections 20, 21, 22
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
Reading: Sections 22, 23, 25
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
Reading: Sections 26, 27, 28
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
Reading: Sections 29, 30, 31
Assignment #12--Due Wednesday, May 4
Exercises: 30.6, 30.7, 30.9, 30.14, 30.15, 30.20, 31.8
Reading: Sections 30, 31
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)
Reading: Section 31