Reference no: EM131103690
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 bn of the Fourier Series using the same technique that we used in class to find an. 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.
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