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)
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 a0/2, rather than a0): 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 bn'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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