- The student is familiar with the fundaments of the theory of Fourier series, of the Fourier transform, and of the finite Fourier theory.
- The student knows the most important theorems, like the inversion theorem, the Parseval/Plancherel formula and Poisson summation.
- The student is able to recognize situations where the theory applies and can use it for solution of a broad class of partial differential equations.
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This course is based on a recent book by Elias Stein, one of the best known exports in the field of Fourier analysis, also known as harmonic analysis. Fourier analysis begins with the idea of Fourier that "every" periodic function is an (infinite) linear combination of sine and cosine functions, but quite some work is required in order to make this idea precise. These Fourier series, as well as the Fourier transform, have many applications to (partial) differential equations and even to number theory!
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Analysis 1 + 2 (possibly also students of physics that have followed Calculus A and B). |
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Written exam (and weekly assignments)
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