HW1: Math 132 PDE II
Due on April 9th during class
(1) Solve the rst order equation 2ut + 3ux = 0 with initial condition u(0, x) = sin x.
Solution: the equation is written as ut + 3/2ux = 0, and since we have u(0, x) = sin x,
the solution is given by u(t,
HW3: Math 132 PDE II
Due on April 23rd during class
(1) Consider waves in a resistant media that satises the problem
utt = c2 uxx rut , x (0, l)
with boundary condition u(t, 0) = u(t, l) = 0 and initial condition u(0, x) = (x), ut (0, x) =
(x). Here r is
HW2: Math 132 PDE II
Due on April 16th during class
1A (x) is the indicate function for set A R, i.e., 1A (x) = 1 if x A and 1A (x) = 0 if x A.
/
(1) Solve the wave equation utt = uxx with u(0, x) = ex and ut (0, x) = sin x.
Solution: By applying dAlember
HW4: Math 132 PDE II
Due on April 30th during class
(1) Find the Fourier cosine series of the function | sin x| in the interval (, ). Use it to nd
the sums
1
(1)n
and
.
4n2 1
4n2 1
n=1
Solution: We write | sin x| =
Bn =
1
| sin x| cos nxdx =
2
1
2 B0
n=1