HW 8
1) The Fourier series of a Sin function should be trivial, right? Execute the following Mathematica code. Explain the result.
FourierTrigSeries[Sin[x], x, 4]
Remember to load the appropriate library before you try this.
2) Look at problem 5.2 in Chapter 7 of Boas. Verify the first nonzero Sin and Cosine terms by doing the integrals by hand. Then show the precise call to FourierTrigSeries that will reproduce the 8 terms shown in the answer. This will require to look carefully into the definitions used by Mathematica and the optional arguments of FourierTrigSeries.
3-4) Chapter 7, section 10 of Boas: Problems 4 and 9.
5) Prove Equation 11.5 on page 375.
6) Show that this function is normalized. That means that when you integrate it from -infinity to +infinity you get 1: Failed to parse (Cannot write to or create math temp directory): 1/(\sqrt[2 \pi] \sigma) Exp[-(t - m)^2/(2 \sigmas^2)]
