Engineering Mathematics 2-Homework 6
Exam 1(5 pages5 Exercises100 points)
February 27, 2013
SOLUTIONS
Instructions.
SHOW ALL YOUR WORK! and write clearly.
witchcraft will not get any credit.
Results obtained by divine inspiration, magic or
Try to write
Engineering Mathematics 2
Exam 2
March 27, 2013
Solutions
Notice that exercises 1+3 = 1+4 =70 points.
1. (50 points, so try not to mess up) Solve by separation of variables
utt (x, y, t)
u(0, y, t)
u(x, 0, t)
u(x, y, 0)
ut (x, y, 0)
=
=
=
=
=
uxx (x, y, t
Engineering Mathematics 2
Final exam-Study guide
The nal exam on Sunday, April 28, at the convenient time of 6:45 to
9:15 PM, in GS 101.
Ill be in my oce, to answer questions, Friday, April 26, at approximately 10AM. I may or may not get lunch after that,
Engineering Mathematics 2-Homework 3
Solutions
Homework 3 consisted of Exercises 1-8 of Chapter 3, pages 54-55, of the textbook. Exercises 1 to 6 one had
to verify that a given problem was an S-L eigenvalue problem, and decide if it was regular or not. It
Engineering Mathematics 2-Quiz 1
Friday, January 18, 2013
SOLUTION
For the function dened by
1, 1 x 0,
0, 0 < x 1,
f (x) =
construct the full Fourier series (50 points), discuss the convergence of this series on the interval [1, 1] (do not
forget the endp
Engineering Mathematics 2-Quiz 4
Friday, February 22, 2013
Solutions
1. (90 points) Solve
utt = uxx ,
u(0, t) = 0,
0, x < 1,
t > 0,
u(1, t) = 0,
u(x, 0) = sin 3x,
t > 0,
ut (x, 0) = 0.
Solution.
Using DAlemberts formula, one can write out the solution at
Quiz #6
Wednesday April 17, 2013
Solutions
Suppose we have the series
cn einx ,
x=
1 < x < 1.
n=
(a) Determine cn , n = 0, 1, 2, . . .
(b) Does the series converge for x = 1? If yes, to what?
(c) Does the series converge for x = 1.5? If yes, to what?
Sol
Engineering Mathematics 2-Homework 6
Sample Exam 1
The topics for exam 1 are: Fourier Series (including sine and cosine series), Sturm-Liouville problems, separation
of variables. This is a lot of topics for a one hour exam. Expect the exam to be more on
Sample Exam 2
Topics for Exam 2 are: DAlembert solution of the wave equation; Laplace equation in a rectangle or a disk,
the rectangular and circular vibrating membranes, and Chapter 6 of the textbook.
1. Solve the problem
utt (x, t) = c2 uxx (x, t),
0 <