570.661 Applied Mathematics for Engineering
Homework Set 11: Due November 27 or 29, 2012
Problems which will be graded:
1. Solve
2u 2u
+
=0
x2 y 2
with the boundary conditions as shown (0 x a,
0 y b):
u = T1
u=0
u/x = 0
u/y = q
The solution will be given

570.661 Applied Mathematics for Engineering
Homework Set 12: Due December 7, 2012 (last day of classes)
Problems which will be graded:
1. Solve
1 2u
2 u 1 u
= 2+
(1)
c2 t2
r
r r
The boundary conditions are u(r = a, t) = 0. The initial conditions are u(r,

570.661 Applied Mathematics for Engineering
Homework Set 10: Due November 20, 2012
Problems which will be graded:
1. Using the method of Laplace transformation, solve the following initial value problem:
y 5y + 4y = 9et
y (0) = 1
y (0) = 2
2. Obtain the g

570.661 Applied Mathematics for Engineering
Homework Set 9: Due November 13, 2012
Problems which will be graded:
1. Using the shifting theorems determine the inverse Laplace transforms of
G (s ) =
G (s ) =
G (s ) =
1
s1
1
(s 1)2
1 st
e
where t > 0
s+1
1 e

570.661 Applied Mathematics for Engineering
Homework Set 8: Due November 6, 2012
Problems which will be graded:
1. Determine the Fourier series of the following function with periodicity p = 2 :
f (t) = t2
where < t < .
Practice problems which will NOT be

570.661 Applied Mathematics for Engineering
Homework Set 7 due October 30, 2012
Problems which will be graded:
1. Consider the following ODE:
xy + 2y + 4xy = 0
Using Frobeniuss method, derive a solution for the larger root of the
indicial equation.
Note t

570.661 Applied Mathematics for Engineering
Homework Set 6 due October 18, 2012
Problems which will be graded:
1. Consider the following ODE with variable coecients:
y + y = 0
Assume that the solution is given by a power series about the point
x = 0:
y=
a

570.661 Applied Mathematics for Engineering
Homework Set 4 due October 2, 2012
Problems which will be graded:
1. Solve the following initial value problem:
13
3 7
y =
y
0
1
y (0) =
Practice problems which will NOT be graded:
2. Solve the following initial

570.661 Applied Mathematics for Engineering
Homework Set 3 due September 25, 2012
Problems which will be graded:
1. Find the general solution for the following ODE using the method of
variation of parameters:
y + 2y + y =
2ex
x2
2. Solve the following Eul

570.661 Applied Mathematics for Engineering
Homework Set 2 due September 18, 2012
1. Solve the following initial value problem:
y + 4y + 5y = 0
y (0) = 1
y (0) = 4
2. Obtain the solution to the following initial value problem:
y 7y + 6y = 0
y (0) = 0
y (0