Math 054 partial differential equations - hw assignment 3

Question

Math 054 Partial Differential Equations - HW Assignment 3

1. Explain why for an infinite rod, the auxiliary conditions are u(x, 0) for the heat equation and u(x, 0), ut(x, 0) for the wave equation.

2. Find b_n of the Fourier Series using the same technique that we used in class to find a_n. Hint: Multiply both sides by sin mπx/L.

3. The Sawtooth Function is given by

The Fourier Series expansion is given by

f(x) = _n=1∑^∞(1/n)sin nx

Plot the tenth partial sums of the Fourier Series of the sawtooth function.

4. The 2π periodic triangular wave is given on the interval [-π, π] by

Find its Fourier Series.

5. The 2π periodic function is given on the interval [-π, π] by

Find its Fourier series.