ACM 95/100c Problem Set 5 Solutions
Faisal Amlani, faisal@caltech.edu May 22, 2012
Problem 1 Consider the solution of the heat equation for the temperature in a rod given by (x, t) but with a variable diffusivity: t = A2 x2 , x x where A is a constant. Su

ACM 95/100c Problem Set 5
May 11, 2012
Due by midnight on 5/18/2012 If needed, you can hand in the problem set as late as midnight 5/21/2012 for full credit Please upload a scan or pdf of your problem set via Moodle. Please keep a copy of your problem set

ACM 95/100c Problem Set 2 Solutions
Faisal Amlani, faisal@caltech.edu April 17, 2012
Problem 1 (25 points) Consider the function given by f (x) = (1 - x2 /L2 ) 0 < x < L.
(a) Develop the Fourier sine series over the interval 0 < x < L. (b) Develop the Fou

ACM 95/100c Problem Set 6 Solutions
Faisal Amlani, faisal@caltech.edu May 31, 2012
Problem 1 Solve the heat equation t = a2 xx with initial conditions (x, 0) = 0 and with boundary conditions (0, t) = t/T 0 0<tT t>T t>0 x>0
Use the Laplace transform in com

ACM 95/100c Final exam
June 2, 2012
For seniors: Due by midnight on 6/8/2012
For everyone else: Due by midnight on 6/15/2012
Please upload a scan or pdf of your midterm set via Moodle.
Please keep a copy of your midterm after you have submitted it (just i

ACM 95/100c Problem Set 7 Solutions
Faisal Amlani, faisal@caltech.edu June 4, 2012
Problem 1 Consider the heat equation in three dimensions with no sources but with non-constant thermal properties: u = (K0 u) c t where c, , and K0 are functions of x, y, a

ACM 95/100c Problem Set 7
May 24, 2012
Due by midnight on 6/1/2012
If needed, you can hand in the problem set as late as midnight 6/4/2012 for full credit
Please upload a scan or pdf of your problem set via Moodle.
Please keep a copy of your problem set.

ACM 95/100c Problem Set 6
May 24, 2012
Due by midnight on 5/25/2012
If needed, you can hand in the problem set as late as midnight 5/29/2012 for full credit
Please upload a scan or pdf of your problem set via Moodle.
Please keep a copy of your problem set

ACM 95/100c Problem Set 3 Solutions
Faisal Amlani, faisal@caltech.edu
May 1, 2012
Problem 1 Consider the two point boundary value problem
y + y = x 0 x 1
with boundary condtions y (0) = 0 and y (1) = 0.
(a) (13 points) Solve this problem using an appropri

ACM 95/100c Problem Set 2
April 17, 2012
Due by midnight on 4/20/2012 If needed, you can hand in the problem set as late as midnight 4/23/2012 for full credit Please upload a scan or pdf of your problem set via Moodle. Please keep a copy of your problem s

ACM 95/100c Problem Set 1 Solutions
Faisal Amlani, faisal@caltech.edu
April 17, 2012
Problem 1 (20 points) Using integration by parts, verify the Lagrange identity. That is show that if we
dene the operator
L[y (x)] =
d
dx
p(x)
d
y (x) + q (x)y (x),
dx
a

ACM 95/100c Midterm Solutions
Faisal Amlani, faisal@caltech.edu
May 11, 2012
Problem 1 Consider the ODE
d
dx
x2
dy
dx
1
+ y + y = 0
4
1 x e
with boundary conditions
y (e ) = 0
y (1) = 0
(a) (5 points) Show that the operator associated with this ODE is sel

ACM 95/100c Midterm exam
April 30, 2012
Due by midnight on 5/7/2012 Please upload a scan or pdf of your midterm set via Moodle. Please keep a copy of your midterm after you have submitted it (just in case). The exam has 4 problems each counting for 25 poi