Math 4567

Applied Fourier Analysis

Spring 2012

Unless otherwise indicated all assignments are taken from Fourier Series and Boundary Value Problems, Brown and Churchill, 8th edition.
Homework Assignments
Date DueAssignment
1January 27 Page 12: 1, 3, 4, 8
Page 18: 2, 4
Do problem (AB 1) in this file.
Page 22: 1
Page 33: 1
Page 41: 2, 5
2February 3 Page 33: 3 (Hint: use Problem 9 on page 13. You do not need to do Problem 9 on page 13.)
Page 41: 8
Page 58: 1, 2, 3, 5. If you are asked to "describe a function graphically", it suffices to sketch a graph of that function on the interval (-2π,2π).
3February 10 Do problems (AB 2), (AB 3) and (AB 4) in this file.
Page 67: 1, 2
4February 17 Page 72: 1, 2
Do problem (AB 6) in this file. Do problem (AB 5) if you feel you need a review of cylindrical and spherical coordinates.
Page 78: 2, 4, 5. Notice that Newton's Law of Cooling is defined on page 74.
5February 24
(Midterm 1)
Page 83: 1, 2, 5
Page 90: 3, 4
6March 2 Do problems (AB 7) through (AB 13) in this file.
7March 9 Do problems (AB 14) through (AB 16) in this file.
Page 225: 1, 4, 12a. Solutions need not be normalized.
8March 23 Do problems (AB 17) through (AB 21) in this file.
9March 30 Page 128: 1, 2, 9
Do problems (AB 22) and (AB 23) in this file.
10April 6
(Midterm 2)
Do problems (AB 24) through (AB 27) in this file.
Page 236: 4a.
Do problem (AB 28) in this file.
11April 13 Do problems (AB 29) through (AB 31) in this file.
Page 172: 4. You may use the formula cos(απ-αx)=cos(απ)cos(αx)+sin(απ)sin(αx).
Do problem (AB 32) in this file.
12April 20 Do problems (AB 33) and (AB 34) in this file.
Page 176: 3
Page 181: 3, 6
13April 27
(Midterm 3)
Do problems (AB 35) through (AB 37) in this file.
Page 188: 3. (Your answer may involve the Fourier transform; you don't need to put it in the form shown in the book.)
Do problem (AB 38) in this file.
14May 4 Do problems (AB 39) through (AB 43) in this file. Problems (AB 44) and (AB 45) will not be graded. You are strongly encouraged to do them anyway, as the Cooley-Tukey algorithm will appear on the final exam.
May 12 Final exam, 10:30–12:30.
Remember that all assignments are subject to change up until 3:15 p.m. on Monday.

A good way to plot things is to use WolframAlpha.com.

Some useful documents
(To use these, save to your computer and open using the appropriate application.)
Graphing in Maple, Mathematica, or Mac OS X's "Grapher" application
Some notes on trigonometric functions (PDF)
Answers to selected problems (PDF)
Review problems for Midterm 1 (PDF)
Review problems for Midterm 2 (PDF)
Review problems for Midterm 3 (PDF); Formulas.pdf
Diagram of the FFT, N=8 (PDF)
Review problems for the final exam (PDF) and answers (PDF) (also go over the review problems for the midterms)

Instructor

Name: Ariel Barton
Office: Vincent 459
Email: abarton@math.umn.edu

Syllabus: syllabus.pdf

Office Hours

Vincent 459
Tuesdays beginning at 3:35
Thursdays beginning at 4:40

Important dates

Wednesday,  January 18: First day of class
Friday, February 24,  1:25–2:15: Midterm I
Monday, March 12: Spring Break begins
Friday, March 16: Spring Break ends
Friday, April 6, 1:25–2:15: Midterm II
Friday, April 27, 1:25–2:15: Midterm III
Friday, May 4: Last day of class
Saturday, May 12, 10:30–12:30:  Final exam