18.103
Fourier Analysis: Theory and Applications
Roughly half the subject devoted to the theory of the Lebesgue integral with applications to probability, and half to Fourier series and Fourier integrals.
Fall 2013 · Fourier Analysis
This course continues the content covered in [_18.100 Analysis I_](/courses/18-100b-analysis-i-fall-2010/). Roughly half of the subject is devoted to the theory of the Lebesgue integral with applications to probability, and the other half to Fourier series and Fourier integrals.
Readings
- Stein, Elias M., and Rami Shakarchi. Fourier Analysis: An Introduction . Princeton University Press, 2003. ISBN: 9780691113845.
- Another useful book for reference is: Körner, T. W. Fourier Analysis . Cambridge University Press, 1988. ISBN: 9780521251204.
- Additional notes are provided for selected lectures to supplement the textbook.
- LEC #: 3 · TOPICS: Measurable Functions, Lebesgue Integral · READINGS: Sections 2.1 and 2.2 · LECTURE NOTES: <no notes>
- LEC #: 4 · TOPICS: Convergence Theorems, Riemann Integrability · READINGS: Sections 2.3 and 2.4 · LECTURE NOTES: <no notes>
- LEC #: 5 · TOPICS: Fubini’s Theorem, Independent Random Variables · READINGS: Sections 2.5, 2.6, and 2.7 · LECTURE NOTES: <no notes>
Prerequisites & course information
Subject meets with 18.1031 Prereq: ( 18.06 , 18.700 , or 18.701 ) and ( 18.100A , 18.100B , 18.100P , or 18.100Q ) U (Fall) 3-0-9 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2013
- MIT OCW syllabus ↗
- MIT OCW readings ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.