#
Fourier Analysis (201-1-0231), Spring
2009/10

Lecturer: Ilan Hirshberg

Email address:

Office: Building 58 (Deichmann), room 203.

**Office hours: **
- Sunday 17:15-18:00
- Wednesday 14:15-15:00

**Lectures:**
- Sunday 15:00-17:00, building 90 room 145
- Tuesday 12:00-14:00, building 90, room 241

Course policies

**Midterm:**
The midterm took place on
Sunday, 18/4 at 15:00. Midterm solutions.

Midterm grades.

Final exam

### Problem sets

Problem set #1, due Tuesday 16/3
Solution outlines to selected problems

Problem set #2, due Tuesday 16/3
Solution outlines to selected problems

Problem set #3, due Tuesday 23/3
Solution outlines to selected problems

Problem set #4, due Tuesday 6/4
Solution outlines to selected problems

Problem set #5, due Tuesday 13/4
Solution outlines to selected problems

Problem set #6, due Tuesday 27/4
Solution outlines to selected problems

Problem set #7, due Tuesday 4/5
Solution outlines to selected problems

Problem set #8, due Tuesday 11/5
Solution outlines to selected problems

Problem set #9, due Tuesday 25/5
Solution outlines to selected problems

Problem set #10, due Tuesday 1/6

Problem set #11, due Sunday 13/6
Solution outlines to selected problems

Exams from previous years (note that the syllabus was somewhat
different):
2006-A,
2006-B,
2007-A
(solutions),
2007-B,
2008-A,
2008-B.

- Animated illustrations of the Fejer kernel (first 20 functions) and the Dirichlet kernel (first 15 functions).

- Brief note on two-sided
series

- An animated
illustration of
a Weierstrass-type nowhere differentiable
function. The one shown is with the following parameters:
(thanks due to
Daniel Markiewicz for the nice image).
And here's another animation
I found on the web.

In case you're *really* interested in nowhere differentiable
functions, here's a link to a master's
thesis on the history of nowhere differntiable functions (credit due
to Eitan Sayag for finding it).
- An animated
illustration of
the Gibbs phenomenon. Here you can see the first 30 partial Fourier sums
of the
function f(x)=x (which you analyze in problem set 6, question 2), as the
number of summands increases. Notice the bump on the right.