Mathematics Homework Solutions

Homogeneous PDE

Homogeneous PDE & BC. See attached file for full problem description.

Fourier Sine, Cosine Series 3 Problems

See attached file for full problem description.

Fourier Series Problem

See attached file for full problem description.

Complex Fourier Series

Complex Fourier Series. See attached file for full problem description.

Wave Equation

Wave Equation. See attached file for full problem description.

PDE

For the (i) I have I used the duality of Fourier transform. but I am having trouble. for (ii) I think I can use xf(X) <---> iF'(x) by multiplying x on the result of (i). but you see the on the bottom has ( x^2+a^2)^2, I have no idea how i can transform it. You don't have to worry about (iii)

Fourier Series

See attached file for full problem description.

Wave Equation

Wave Equation. See attached file for full problem description.

Wave Equation

Wave Equation. See attached file for full problem description.

Wave Equation

Wave Equation. See attached file for full problem description.

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