Fourier Analysis, MAN530 / TMA362, 5p

Fall 2006

Literature

[GF] G. Folland: Fourier Analysis and its applications, Brooks/Cole publishing, 1992

The course comprises the following chapters and sections of the book:
Ch. 1; Ch. 2, 2.1-5; Ch.3, 3.1-5; Ch. 4, 4.1-4; Ch. 7, 7.1-4; if possible also Ch. 8, 8.1, 8.3, 8.5 (Slight modifications may occur here.)

The book can be perchased at UBSAB, phone 7116039, Vasagatan 36. One can buy it in connection with the first lecture, 5th September. The price is 550:-

A problem collection [Ö] "Exercises in Fourier Analysis" will also be used and will be handed out.

Syllabus

  1. Fourier series expansion of functions on an interval
  2. The Fourier transform and the Laplace transform
  3. Application to solution methods for ordinary and partial differential equations.

The theory part of the course contains the basic concepts of Fourier analysis, the ideas and techniques used to prove theorems and the underlying principles of the whole theory. The problem and practice part focuses on the applications of the theory to solve differential equations by means of series expansion and transforms.

There will be a written examination at the end of the course.

Lecture/Examinator, Exercise Assistant

Maria Roginskaya, office L2127 at MV, e-mail: maria_at_math.chalmers.se

Mikael Persson, office L2121 at MV, e-mail: mickep_at_math.chalmers.se

Details

Class shedule
List with the theoretical requirements for the exam (plus all the definitions):
    1. Formulas (2.5) and (2.6)
      Bessel's inequality
      Corollary 2.1
    2. Theorem 2.1
      Corollary 2.2
    3. Theorem 2.2
      Theorem 2.4
      Theorem 2.5
      Theorem 2.6
    4. Formulas (2.10) and (2.22)
    3. Bessel's inequality
      Theorem 3.4
      Theorem 3.5
      Parseval's equation
    4. Theorem 3.8
      Corollary 3.1
    5. Theorem 3.8 ab (without proof)
      Theorem 3.10 (without proof)
    1. Theorem 7.3 (only for the point of continuity)
    2. Theorem 7.5
      Fourier Inversion Formula
      Plancherel theorem
    3. Poisson integral formula
      Sampling Theorem
      Heisenberg's inequality