# MA490F Fourier Analysis

Purdue University Spring 2008

## Monday, April 14, 2008

### Midterm Exam 2

Take-home exam. Deadline: Fri, Apr 18

[Midterm Exam 2]

## Wednesday, April 9, 2008

### Homework

All assignments are from [Stein-Shakarchi]

(Note that there are two types of problems in the textbook: Exercises and Problems)

#8 Due Wed 04/09: Chap 5: Exercises 13, 15, 21, Problem 4 (omit part b).
[Partial Solutions]
#7 Due Fri 03/28: Chap 5: Exercises 5, 7, 11, 12, (13 -this problem is postponed until next homework)
#6 Due Fri 03/07: Chap 5: Exercises 1, 2, 3, 4.
#5 Due Fri 02/29: Chap 4: Exercises 1, 4, 7; Problem 4.
(see Theorem 7.18 in Rudin's "Priniciples of Math. Analysis" for more detais on Problem 4 [PDF] )
#4 Due Mon 02/11: Chap 3: Exercises 2, 3, 6, 13, 15
[Partial Solutions]
#3 Due Fri 02/01: Chap 2: Exercises 12, 13(a), 15, 17 (a,b)
[Partial Solutions]
#2 Due Fri 01/25: Chap 2: Exercises 2, 3, 6, 10, 11
#1 Due Wed 01/16: Chap 1: Exercises 5, 7, 8, 9, 11; Problem 1.
[Partial Solutions]

## Wednesday, February 6, 2008

### Midterm Exam 1

Scheduled Tue, Feb 19 7:00-8:30 pm in MATH 211

It will be a 90 min exam, covering the material learned up to Wed, Feb 13 (inclusively).

## Friday, January 25, 2008

### Course Log

Planned
- Fri 02/01: cancelled
- Wed 01/30: Ch 3, pp. 70-76: Review of Vector and Hilbert spaces
- Mon 01/28: Ch 2, pp. 53-58: Abel means and summation, Poisson kernel and Dirichlet problem.

Covered
- Fri 01/25: Ch 2, pp. 48-53: Good kernels, Cesaro means and summation, Fejer kernel.
- Wed 01/23: Ch 2, pp. 44-48: Convolutions
- Mon 01/21: No class (MLK day)
- Fri 01/18: Ch 2, pp. 39-44 : Uniqueness of Fourier series
- Wed 01/16: Ch 2, pp. 34-39: Definition of Fourier series, Dirichlet kernels, uniqueness theorem
- Mon 01/14: Ch 1, pp. 18-23: Heat equation, Laplace's equation, Ch 2, pp. 29-33: Riemann integrable functions, functions on unit circle
- Fri 01/11: Ch 1, pp. 14-19: Fourier sine series, Fourier series, plucked string, heat equation
- Wed 01/09: Ch 1, pp. 10-14: D'Alembert's formula, standing waves, separation of variables.
- Mon 01/07: Ch 1, pp. 1-10: Simple harmonic motion, derivation of wave equation, traveling waves.

## Sunday, January 6, 2008

### Course Information

Time and Place: MWF 11:30am-12:20pm in UNIV 201.
Official Schedule

Instructor: Arshak Petrosyan
Office Hours: MWF 10:30 -11:30am, or by appointment, in MATH 610

Textbook: E.M. Stein & R. Shakarchi, Fourier Analysis: An Introduction, Princeton University Press, 2003.

Syllabus is essentially the first six chapters in [Stein-Shakarchi]:
1. The Genesis of Fourier Analysis
2. Basic Properties of Fourier Series
3. Convergence of Fourier Series
4. Some Applications of Fourier Series
5. The Fourier Transform on R
6. The Fourier Transform on Rd

Homework will be collected weekly on Wednesdays. The assignments will be posted on this website at least one week prior the due date.

Exams: To be specified