Fall 2017

MTH 402, Introduction to Fourier analysis.

SYLLABUS

Time: MW, 1:10 pm – 2:40 pm

Room: Science 205

Instructor: Dr. Arkady Kitover

Office: Science 343 (inside of 340)

Office hours: MWF 12:30 pm – 1:10 pm, or by appointment

Class materials: class materials will be handed over by the instructor during class sessions

Course Contents and Examinations

1. Fourier series of continuous and piecewise continuous functions. Representing functions by their Fourier series. Types of convergence of Fourier series. Examination 1.

2. A very brief introduction to Lebesgue integral. Spaces . Trigonometric and exponential orthonormal bases in . Parseval’s identity. Convergence almost everywhere. Some other orthonormal systems of functions. Examination 2.

3. Fourier transform on and its extension on . Inverse Fourier transform. Plancherel theorem. Examples of Fourier transforms. Examination 3.

4. Applications of Fourier series and Fourier transform. Examination 4.

5. A brief introduction into harmonic analysis on compact and locally compact Abelian groups. Examination 5.

Grading

It will be 5 examinations, 100 points each, and 5 homework assignments, 20 points each. The grades will be assigned as follows.

A: 570 – 600

A-: 540 – 569

B+: 510 – 539

B: 480 – 509

B-: 450 – 479

C+: 420 – 449

C: 390 – 419

C-: 360 – 389

D-: 330 – 359

F: 0 – 329

Class Rules

For every three unexcused absences, the grade will be reduced by one third of a letter.

No food is allowed in the classroom.

You may not use electronic devices for purposes unrelated to the class work (e.g. texting, web surfing, et cetera).

Cell phones must be in the silent mode.

If you are more than 15 minutes late I will consider it as ½ of an unexcused absence.