Name:

MATH 285 Section N1
Fall 2001
Quiz 7

Please answer all questions on this sheet (note that there is a question on the back as well). You must show your work to obtain full credit. 10 points are possible. Good luck!

1.

(5 points) Solve the heat equation u_t=3u_xx

with boundary conditions u(0,t)=0, u(2,t)=0, u(x,0)=f(x)

where f(x) has Fourier sine series (1/1³)sin(1px/2)+ (1/2³)sin(2px/2)+ (1/3³)sin(3px/2)+...

2.

(5 points) Solve the wave equation y_tt=4y_xx

with boundary conditions y(0,t)=0, y(p,t)=0, y(x,0)=f(x), y_t(x,0)=0

where f(x) has Fourier sine series (2/1²)sin(x)+ (2/2²)sin(2x)+ (2/3²)sin(3x)+...