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

Lecturer: Ilan Hirshberg
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.
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: $f(x)=\sum_{n=0}^{\infty}\frac{1}{2^n}\cos (3^n x)$ (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.