Mathematics Department

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*Course #: 50356**Class meets:*Tue & Thu 1:15-2:30 p.m. in Yost 321B*Instructor:*Stanislaw J. Szarek (pronounced 'Sharek')*Office:*Yost 320*Office hours:*Currently T 2:30-3:30, W 10:30-11:30 or by appointment (or by luck - just drop by, I am in most of the time)*Phone:*368-2913*E-mail:*sjs13@po.cwru.edu Asking questions by e-mail is particularly encouraged.*WWW Home Page:*http://www.cwru.edu/artsci/math/szarek/*Class WWW Page (this page):*http://www.cwru.edu/artsci/math/szarek/MATH428/*Prerequisite:*MATH 224; in addition, MATH 321 and/or MATH 201 are recommended.*Text:*"Fourier Analysis" by James S. Walker; Oxford University Press 1988. ISBN 0-19-504300-6.

Additional notes may be supplied for extra topics.

"Fourier Analysis" by T. Körner could be a good supplementary reading for the more inquisitive minds.

**What is Fourier Analysis:** Fourier Analysis is a vast area of
mathematics which originated in early 19th century with study of physical
phenomena such as heat conduction and waves.
*Some * aspects of Fourier Analysis
are indispensable in virtually any area of science and engineering.

**Material to be covered: ** In principle, chapters 1, 2, 3, 6 and 7
and elements of chapter 8 of the textbook, not necessarily in that order.
Roughly speaking, this involves a relatively elementary discussion of Fourier
series and transforms. (See also the official
Course Description.) Depending on the audience, we may
start with a motivational discussion of boundary value problems
(which used to be, but are not now, covered in Math 224).
Later in the semester - even though this is not the main object of the course -
we shall look at the connections to Sampling (a la signal processing),
Fast Fourier Transform and Wavelets.

**Computing & CWRUnet:** This is not a course about computational
or numerical aspects of Fourier Analysis, but * some * of the topics or
concepts shall be presented using mathematical software like
* Matlab,* * Mathematica * or * Maple *
(available on CWRUnet) and * some *
assignments will be most easily done with a computer.
Additionally, I expect most of the 'out of class' course related
communications to occur over the Internet.
(If you are reading this on WWW, that should not be a problem.)

**Grades:** Your Final Grade in the course will be based on
Attendance/Homework/Class Participation (30%), two take-home
Exams (Midterm and Final, 20% & 30%)
and a Presentation (20%).

**Midterm and Final Exams:** A set of problems to work out
**on your own** over a 48/72 hours period.

**Presentation:** A 30-45 minutes presentation of a topic
not covered in detail in class. There may be extra credit if you choose
a tough one.

**Homework:** There will be
homework assigned approximately once per week, due the following week.
Discussing the assignments is allowed, but everybody is responsible for
'verbalizing' and writing up their solutions. These assignments are not expected
to be 'too substantial'.

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