Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 129: Fourier Analysis
Approved: 2006-03-10, Naoki Saito, Thomas Strohmer, and John Hunter

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Fourier Analysis and Its Applications, Gerald Folland, Brooks/Cole, ITP, 1992 ($81)
Search by ISBN on Amazon: 0534170943

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

Week 1

Chapter 1, Section 2.1-2.2

Overture/Motivations; Fourier series of a periodic function; A convergence theorem.

Week 2

Section 2.3, 2.4, and 2.6

Derivatives, integrals, and uniform convergence; Fourier series on intervals; Remarks including the Gibbs phenomenon.

Week 3

Section 3.1-3.3

Othogonal sets of functions; Inner products; Convergence and completeness.

Week 4

Section 3.4-3.5

L^2 spaces; Regular Sturm-Liouville problems.

Week 5

Section 4.1-4.3

Some boundary value problems; 1D heat flow and wave motion.

Week 6

Section 4.4-4.5

The Dirichlet problem; Multiple Fourier series; Good time to do midterm; Coverage should be Chapters 1-4.

Week 7

Section 7.1-7.2

The Fourier transform; Convolution

Week 8

Section 7.3

Applications of Fourier transforms.

Week 9

Section 7.5; Other applications

The Fourier transform of several variables; Various applications.

Week 10

Other applications; Choose from Section 2.5, 6.1-6.2; Section 6.6; Section 7.4; Section 7.6; Section 8.1-8.3

Fourier series and boundary value problems; Orthogonal Polynomials; Haar and Walsh functions; Fourier transforms and Sturm-Liouville problems; Laplace transform and its inversion, etc.

Additional Notes:

After 7th Week, an instructor can freely choose various applications of interest. Other possible sources are:

• H. Dym and H.P. McKean: Fourier Series and Integrals, Academic Press, 1972.
• T.W. Korner: Fourier Analysis, Cambridge Univ. Press, 1988.
• E.M. Stein and R. Shakarchi: Fourier Analysis, Princeton Univ. Press, 2003.
• J.S. Walker: Fourier Analysis, Oxford Univ. Press, 1988