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**Unformatted text preview: **MATH 412: Problem Set 5 due Thursday, March 27, 2008 1. Strauss 4.1 #3 - Schrdinger equation o 2. Strauss 4.2 #1 - diffusion equation with mixed Dirichlet-Neumann BCs 3. Strauss 4.2 #4 - diffusion equation with periodic BCs 4. Consider the function f (x) = |x| on the interval [-1, 1], a triangle. (a) Find the Fourier series for this function (b) Sketch the periodic extension of f to the entire real line. Is this what you would get if you evalulate the Fourier series outside of [-1, 1], or would you get something else? 5. Strauss 5.1 #5 - integrating a Fourier series - (use Eq. 12 from 5.1) 6. Strauss 5.2 #1 - function symmetries 7. Strauss 5.2 #2 - periodicity of two cosines - if you can, illustrate by plotting some of the cases, and include your plots ...

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