Math
4567 : Applied Fourier
Analysis (Lecture 001)
Fall Semester 2009, 12:20  13:10 pm, MWF, VinH
20
Prereq Math 2243 or 2373 or 2573;
4 credits
Instructor: Willard
Miller
Office: Vincent Hall 513
VinH
Office Hours: 01:25
P.M.02:15 P.M. (M,F) , 11:15
A.M.12:05 P.M. (W),
or by appointment
Phone: 6126247379
miller@ima.umn.edu,
miller@math.umn.edu
The Math
Library 4567 CourseLib page
Textbook: Fourier Series and Boundary Value problems, by James Ward Brown and Ruel V. Churchill, McgrawHill, New York, 2008 (7th edition).
Class Description: This is a basic course on the representation and approximation of arbitrary functions as infinite linear combinations of simple functions, and of the applications of this idea in the physical and engineering sciences. Topics include: Orthonormal functions, best approximation in the mean, Fourier series, convergence pointwise and in the mean. Applications to boundary value problems, SturmLiouville equations, eigenfunctions, Fourier transform and applications. As time permits: Complex Fourier series and Fourier transform, FFT, Gibbs phenomena, Caesaro sums.
Policies:
Content and Style: Will cover most of Chapters 18. Homework
assignments from the textbook, and from my own notes. The theory
will predominate, but there will be considerable attention to
applications in other fields. Notes, homework assignments, examples,
practice exams, etc., will be posted online as the course develops.
Student Conduct: Statement on Scholastic Conduct: Each
student should read the college bulletin for the definitions and
possible
penalties for scholastic dishonesty. Students
suspected of cheating will be reported to the Scholastic Conduct
Committee.
Week 

Chapter 
HW due  
W  SEP 09  1  Orthonormal Sets 
7 

F  SEP 11 
1  Orthonormal Sets  7 

M  SEP 14  2  Orthonormal Sets  7 

W  SEP 16  2  Introduction to Fourier Series 
1  
F  SEP 18  2  Introduction to Fourier Series 
1 

M  SEP 21 
3  Introduction to Fourier Series 
1 

W  SEP 23 
3  Convergence of Fourier Series 
2 

F  SEP 25  3  Convergence of Fourier Series  2 

M  SEP 28  4  Convergence of Fourier Series  2 

W  SEP 30 
4  Convergence of Fourier Series  2 

F  OCT 02 
4  Convergence of Fourier Series  2 
#1 

M  OCT 05  5  Partial Differential Equations of Physics 
3 

W  OCT 07  5  Partial Differential Equations of Physics  3 

F  OCT 09  5  Midterm 1 

M  OCT 12 
6  Partial Differential Equations of Physics  3 

W  OCT 14  6  Partial Differential Equations of Physics  3 

F  OCT 16  6  Partial Differential Equations of Physics  3 
#2 

M  OCT 19  7  Partial Differential Equations of Physics  3 

W  OCT 21 
7  The Fourier Method  4 

F  OCT 23 
7  The Fourier Method  4 

M  OCT 26  8  The Fourier Method  4 

W  OCT 28  8  Boundary value Problems  5 

F  OCT 30 
8  Boundary value Problems  5 
#3 

M  NOV 02 
9  Boundary value Problems  5 

W  NOV 04 
9  SturmLiouville Problems and Applications  8 

F  NOV 06  9  SturmLiouville Problems and Applications  8 

M  NOV 09  10  Midterm 2 

W  NOV 11 
10  SturmLiouville Problems and Applications  8 

F  NOV 13 
10  SturmLiouville Problems and Applications  8 
#4 

M 
NOV 16 
11 
SturmLiouville Problems and Applications  8 

W  NOV 18  11  SturmLiouville Problems and Applications  8 

F  NOV 20 
11  SturmLiouville Problems and Applications  8 

M  NOV 23 
12  SturmLiouville Problems and Applications  8 

W  NOV 25  12  Fourier Integrals and Applications  6 

F  NOV 27  12  Thanksgiving Vacation  
M  NOV 30 
13  Fourier Integrals and Applications  6 

W  DEC 02 
13  Fourier Integrals and Applications  6 

F  DEC 04 
13  Fourier Integrals and Applications  6 
#5 

M  DEC 07  14  Midterm 3 

W  DEC 09  14  Fourier Integrals and Applications  6 

F  DEC 11 
14  Fourier Integrals and Applications  6 

M  DEC 14 
15  Fourier Integrals and Applications  6 

W  DEC 16  15 



M 
DEC 23 
Final Exam, (last day for turning in the take home exam,
my office) 
Graphs
of some Taylor polynomial approximations of sin(x), 4 < x
< 4. Note that the Taylor polynomial T_19(x) is
such a good approximation that the graphs can't be distinguished in the
interval 4 < x < 4.
Maple plots of examples of uniform and nonuniform convergence
Lecture
notes on Fourier series (PDF file) These are taken from
material (copyright by Steve Damelin and Willard Miller) for a more
advanced course. They contain detailed information about Gibbs
phenomena, Cesàro sums and other topics.
Lecture
notes on the Fourier transform (PDF file)
These are taken from material (copyright by Steve Damelin and Willard
Miller) for a more advanced course.
Lecture Notes and Background Materials on Linear Operators in Hilbert Space (pdf file) ( postscript file)