School of Mathematics

University of Minnesota

Instructor: Sasha Voronov

Time: MWF 11:15-12:05

Room: VinH 2

Office Hours: Wed 12:15-1:45 pm, Thu 4:30-6:00 pm, or by appointment (VinH 324)

Grader: Hao Feng, phone: (612) 625-8553, office: VinH 422, e-mail: fengx055@math.umn.edu, tutorial hours in 150 Lind Hall: Mon 2:30 - 3:20, Wed 8:00 - 8:50 & 2:30 - 3:20, and Fri 9:05 - 9:55.

Final Exam: 01:30pm - 03:30pm Saturday, May 12, Vincent Hall 2 (our regular classroom)

Class Outlines

Midterm Exam 1 with Solutions: Page 1, Page 2, Page 3, and Page 4

Solutions to the Other Sample Exam 2

Midterm Exam 2 with Solutions: Page 1, Page 2, Page 3, and Page 4

Final Exam Practice Problems 1 (Misprint in Problem 2: insert a factor of √2 in front of the right-hand side.) Solutions

Final Exam Practice Problems 2 with Solutions (Note: Solutions are at the end of the file. It is most effective to solve the problems without looking the solutions up. Problems 12-17 and E are not covered by our Final Exam). Solutions to selected problems from Part II.

Final Exam Practice Problems on Fourier Series (Problems 2, 4 are not
covered by our Final Exam; In Problem 6 the series for F(x) should
start with a_{0}/2, rather than a_{0}): Page 1, Page 2,
and Page 3. Solutions

Homework 1, due Friday, January 26: Section 1.1: 2(b), 5, 6; Section 1.2: 4, 6, 9

Homework 2, due Friday, February 2: Section 1.2: 2; Section 1.3: 3, 5, 6, 7, 8

Homework 3, due Friday, February 9: Section 1.4: 2, 3, 6, 7; Section 1.5: 1(a,b), 4

Homework 4, due Friday, February 16: Section 1.5: 9, 11; Section 1.6: 1, 2, 4, 6(a,c)

No homework due February 23. Suggested problems for Section 1.7: 3, 4, 10 (not to hand in). Solutions

Homework 5, due Friday, March 2: Section 1.8: 3, 4; Section 2.1: 1, 2, 3, 6 (Show the first identity only)

Homework 6, due Friday, March 9: Section 2.1: 4 (do not show discontinuity), 5; Section 2.2: 1, 3, 5, 6. Solutions

Homework 7, due Friday, March 23: Section 2.2: 2, 8; Section 2.3: 2, 5, 6; Section 2.4: 2. Solutions

Homework 8, due Friday, March 30: Section 2.5: 6; Section 2.6: 9; Section 2.7: 2, 7, 8, 9. Solutions

Homework 9, due Friday, April 6: Section 2.9: 5, 6, 9 (Use Lagrange's method. Bonus question (i.e., a hard question, the bonus being your own satisfaction in cracking a hard problem): why does not solving the constraint first work here?), 13, 14, 15 (misprint in the answer in the first two printings). Solutions

No homework due April 13. Suggested problems (not to hand in): Section 3.1: 3, 5, 7, 9 (misprint in 9 in some printings); Section 7.1: 1, 2, 3, 4, 5 (misprints on pages 315, 317, and answer to 2 in some printings). Solutions

Homework 10, due Friday, April 20: Section 7.3: 3, 5a, 7; Section 8.1: 2, 4, 5, 9 (only do the proof based on breaking up the integral and making a change of variable; you may take a = π/3, if that makes it simpler for you). Solutions

Homework 11, due Friday, April 27: Section 8.2: 4a (you may use the answer to Ex. 8.1.3 posted with Solutions to the previous homework), 4b, 4c; Section 8.3: 3, 4, 5, 6 (note misprints on pages 376 and 377 in some printing). Solutions: Page 1 and Page 2

Homework 12, due Friday, May 4: Section 8.5: 1, 2, 3 (Ignore the
question of validity; also, instead of (8.35), the text should refer
to the top formula on p. 388 with the b_{n}'s included, as
indicated by the list of misprints.), and 4. Solutions (Misprint in Solution to Problem 2:
√α = n, rather than 2πn.)

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