Spring 2015 MATH 8260 Homework 1
This homework was due on Thursday, February 12, in class.
1. Find the solution of the initial value problem
ut + b u + cu = 0 x Rn , t > 0
u(x, 0) = g(x)
x Rn
where b Rn is a constant vector, c is a constant and g C 1 (Rn
Spring 2015 MATH 8260 Homework 1
Please write down all your work and solutions for the following problems.
This homework is due on Thursday, February 12, in class.
1. Find the solution of the initial value problem
ut + b u + cu = 0 x Rn , t > 0
u(x, 0) =
Spring 2015 MATH 8260 Homework 2
Please write down all your work and solutions for the following problems.
This homework is due on Thursday, February 26, in class.
1. Find the general solution of the equation
y 2 uxx 2yuxy + uyy = ux + 6y.
2. Find the sol
Spring 2015 MATH 8260 Homework 3
Please write down all your work and solutions for the following problems.
This homework is due on Tuesday, March 24, in class.
1. Consider the initial value problem for the wave equation in R2 and R3
utt (x, t) c2 u(x, t)
Spring 2015 MATH 8260 Homework 2
This homework was due on Thursday, February 26, in class.
1. Find the general solution of the equation
y 2 uxx 2yuxy + uyy = ux + 6y.
Sol: This is a principally linear equation with a = y 2 , b = 2y and c = 1. So we have
b
Spring 2015 MATH 8260 Homework 3
This homework was due on Wednesday, March 25.
1. Consider the initial value problem for the wave equation in R2 and R3
utt (x, t) c2 u(x, t) = 0
x Rn , t > 0
u(x, 0) = g(x), ut (x, 0) = h(x). x Rn , n = 2, 3.
Suppose that