MATH4822E Fourier Analysis and Applications

Course instructor: Edmund Y.-M. CHIANG
Lecture hours: Tuesday, Thursday 10:30--11:50 (room  4503).
Tutorial: Friday 16:00-16:50 (room 2463)
Email: machiang@ust.hk

Overview: This course studies both the methods and theory of Fourier series, essentially started by J. Fourier in the 19th century. The Fourier method/analysis, as we understood today, is a major tool in solving many classical physical problems. Moreover, the subject gave birth to all kinds of convergence problems in mathmatical analysis that students may encounter in some pure mathematics courses (this includes, e.g.,  Riemann's integration, Cantor's work on countability, etc). If a student wonders why people always claim that mathematics is useful, then this is a course that one could have a glimps of why this is the case. He/she could also have a chance to see some beautiful and yet very useful mathematics. This course uses physical problems and applications to illustrate the important mathematical theoreis behind, not the other way around. This is not a mathematical method course.

Prerequisite: We assume some knowledge of basic mathematical analysis, multivariable calculus. Previous knowledge on differential equations and/or complex analysis will be an advantange but students who have not done these courses may still take this course subject to the approval of the course instructor.

Main reference books:

1. G. B. Folland, ``Fourier Analysis and its Applications", Brooks/Cole Publishing Company, 1992. Republished by American Mathematical Society
2. G. P. Tolstov, ``Fourier Series", Dover publication, 1976.

Distribution of marks (tentative): Homework (15%), mid-term examination (25%) and Final examinaiton (60%).

Tentative topics:

1. Physical application problems
2. Fourier series
3. Orthogonality and completeness
4. Boundary value problems
5. Bessel functions
6. Orthogonal polynomials
7. Fourier transforms

Lecture notes: Lectrue notes will be distributed during the lectures.