MECE 6384
Assignment 1
Spring 2015
Assignment should be completed by Feb 1. Solutions will be posted on blackboard on that date. Graded assignments are due on Feb 3.
Each question carries 10 points.
1. True of False:
a) The set of odd integers is a linear

MECE 6384
Assignment 5
Spring 2015
Graded assignments are due on March 11, Wednesday.
Each question carries 10 points.
1. Complete the derivation started in class for the gradient and divergence of a vector
field in polar coordinates.
2. Derive the expres

MECE 6384
Assignment 4
Spring 2015
Graded assignments are due on Feb 25, Wednesday.
Each question carries 10 points.
1. Let v be a smooth vector field and f and g be smooth scalar fields defined on a region
R in R3 . Let the boundary of the region R be a

MECE 6384
Assignment 3
Spring 2015
Graded assignments are due on Feb 18, Wednesday.
Each question carries 10 points.
1. Consider the matrix
1 1 3
A = 1 5 1
3 1 1
Verify the spectral decomposition theorem using eigenvalues and eigenvectors of A.
2. Show th

MECE 6384
Assignment 9
Spring 2015
Graded assignments are due on April 6, Wednesday.
Each question carries 10 points.
1. Solve the following PDEs by separation of variables:
u
u
x
=0
a)
x
y
u
u
2y
=0
b) x
x
y
2. Consider a vibrating string of length l. T

MECE 6384
Assignment 7
Spring 2015
Graded assignments are due on April 8, Wednesday.
Each question carries 10 points.
1. Find the Fourier transform of H(x a)ebx , where H(x) is the Heaviside function.
2. The one-dimensional neutron diffusion equation with