# 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
Prerequisites:
(MAT 022A or MAT 027A or MAT 067 or BIS 027A); (MAT 022B or MAT 027B or BIS 027B).
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.