# Math 401/501, Advanced Calculus I Spring 2013

## General Information

Instructor: Matthew Blair
Course Web Page: http://www.math.unm.edu/~blair/math401_s13.html
Office: SMLC 330
Office Hours: Tuesdays 10:30-11:30am and 5-6pm. Also 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: Malik Barrett (malikb ["at"] unm.edu)

Course Description (from the catalog): Rigorous treatment of calculus in one variable. Definition and topology of real numbers, sequences, limits, functions, continuity, differentiation and integration. Students will learn how to read, understand and construct mathematical proofs.

Prerequisites (from the catalog): 264 and two courses at the 300+ level.

Course Syllabus (in .pdf format, not posted yet)

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Homework

Assignment #1--Due date Thursday, January 24

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

Assignment #2--Due date Thursday, January 31

Exercises: 6.10, 6.11(a,b,c,h), 6.14, 7.6, 7.7(a,b,e,f), 7.9, 7.10, 7.12, 7.14, 7.15, 7.26, 7.27, 7.29

Assignment #3--Due date Thursday, February 7

Exercises: 8.3(b,d,e), 8.4, 8.7, 8.10, 8.11, 10.3, 10.7, 10.21(a,c), 10.22, 10.25
Reading: Sections 8, 10, 11, 12

Assignment #4--Due date Thursday, February 14

Exercises: 11.3(a,m), 11.4, 11.5, 11.6, 11.7, 12.6, 12.7, 12.12(a,b), 12.13
Reading: Sections 11, 12, 13, 14

Assignment #5--Due date Thursday, February 21

Exercises: 13.3(a,b), 13.4(a,b), 13.5(a,b,c), 13.14, 13.15, 14.3(a,b,c), 14.4, 14.5, 14.8
Notes: In addition to the exercises above, make sure you are able to prove that any open interval (a,b) is an open set.

Assignment #6--Due Thursday, March 7

Exercises: 16.7(c,f), 16.8(a,c), 16.11, 16.12, 16.15, 16.16(a), 17.3, 17.5(f), 17.6(c,d), 17.17
Reading: Sections 16, 17, 18, 19

Assignment #7--Due Thursday, March 21

Exercises: 18.3(a,e), 18.13, 18.15, 19.4, 19.7(a,b), 19.9, 19.10, 19.12, 19.17
Reading: Sections 18, 19, 20, 21

Assignment #8--Due Thursday, March 28

Exercises: 20.3(d,e,g,h), 20.7(c), 20.9, 20.15, 20.18, 21.4, 21.10, 21.13, 21.18
Reading: Sections 20, 21, 22, 23
Notes: On your own (meaning you do not need to address this in your write up), note the connection between Exercise 21.13 and Exercise 20.16. Also, make sure you justify your answers to 20.3(d,e,g,h).

Assignment #9--Due Thursday, April 4

Exercises: 22.5, 22.9, 22.11, 22.13(a), 23.3, 23.4(a,b), 23.11
Reading: Sections 22, 23, 25, 26
Notes: In 23.3, you may assume that the exponential function and the sine function are both continuous functions, leaving you to address the issue of uniform continuity.

Assignment #10--Due Thursday, April 18

Exercises: 25.3, 25.6, 25.7(a,b,d), 25.9, 26.8, 26.15, 26.20, 26.21, 27.4(c,e,f), 27.11
Reading: Sections 25, 26, 27, 28

Assignment #11--Due Thursday, April 25

Exercises: 27.7, 29.5, 29.10, 29.11, 29.13, 29.15, 29.16
Reading: Sections 29, 30, 31, 28
Notes: Observe that Exercise 29.11 can help you answer 29.5. Also, observe that 29.13 yields a quick solution to 30.5.

Assignment #12--Due Thursday, May 2

Exercises: 30.7, 30.8, 30.9, 30.15, 30.20, 31.5(c,d), 31.13, 31.15, 31.17(a,b,d)