MATH 456
Instructor V. E. Zakharov
Homework 2
Due February 18, 2015
1. Solve the heat equation
ut = uxx
on the interval 0 < x < L, subject of boundary conditions
ux |x=L = 0
u|x=0 = 0,
Initial data are the following:
cfw_
1 0 < x < L/2
0 L/2 < x < 1
u0 (x
MATH 456
Instructor V. E. Zakharov
Homework 3
Due March 6, 2015
1. Solve the wave equation
utt = c2 uxx
on the interval 0 < x < l with periodic boundary conditions
u(l) = u(0),
ux (l) = ux (0)
and initial data
u|t=0 = u0 (x) =
n=
un eikn x ,
kn =
n=
ut |t