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
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Lecture(s) |
Sections |
Comments/Topics |
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Week 1 |
Chapter 1, Section 2.1-2.2 |
Overture/Motivations; Fourier series of a periodic function; A convergence theorem. |
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Week 2 |
Section 2.3, 2.4, and 2.6 |
Derivatives, integrals, and uniform convergence; Fourier series on intervals; Remarks including the Gibbs phenomenon. |
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Week 3 |
Section 3.1-3.3 |
Othogonal sets of functions; Inner products; Convergence and completeness. |
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Week 4 |
Section 3.4-3.5 |
L^2 spaces; Regular Sturm-Liouville problems. |
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Week 5 |
Section 4.1-4.3 |
Some boundary value problems; 1D heat flow and wave motion. |
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Week 6 |
Section 4.4-4.5 |
The Dirichlet problem; Multiple Fourier series; Good time to do midterm; Coverage should be Chapters 1-4. |
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Week 7 |
Section 7.1-7.2 |
The Fourier transform; Convolution |
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Week 8 |
Section 7.3 |
Applications of Fourier transforms. |
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Week 9 |
Section 7.5; Other applications |
The Fourier transform of several variables; Various applications. |
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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. |
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