Use the double Fourier series \"generalized Euler formula\" to find the deflection $u(x, y, t)$ of a
membrane with the following conditions:
1. The membrane is square with sides of $\pi$, the initial velocity is 0, and initial deflection is
$2 \sin(2x) \sin (3y)$
2. Use length of the membrane along x is 1 and along y is 2. The initial velocity is 1 and the
initial deflection is $0.1 \sin(3\pi x) \sin(\pi y) (1 - x)(2 - y)$
Use MATLAB to plot the deflection at equally spaced 12-time steps for both problems within the
first 2 seconds.
3. Solve the Laplace equation $U_{xx} + U_{yy} = 0$ in the following domain using the boundary
conditions provided. Plot the solution using the surf command in MATLAB