MATH 337
Assignment 2 - Solutions
(1) The solution is (see the derivation in the lecture notes, and/or the text):
2
bn en t sin(nx)
u(x, t) =
n=1
with coecients
2
bn =
cos(x) sin(nx)dx
0
1
=
[sin(n
Math 337 - Practice Problems #3
Instructions: These problems are practice for the test problems. You may assume that you will
be provided with:
The formulas on the Practice Problems 3 Reference sheet
Math 337 - Practice Problems #2
Instructions: These problems are practice for the test problems. You may assume that you will
be provided with:
The formulas on the Practice Problems 2 Reference sheet
Math 337 - Practice Problems #1
Solutions
Instructions: These problems are practice for the test problems. You may assume that you will
be provided with:
The formulas for the probability distribution
Math 337 - Practice Problems #3
Solutions
Instructions: These problems are practice for the test problems. You may assume that you will
be provided with:
The formulas on the Practice Problems 3 Refer
STUDENT NUMBER:
Page 1 of 6
MATH 337 - Test 2
INSTRUCTIONS:
Answer all questions, writing clearly in the space provided. If you need more room, continue your
answer on the back of the page, providing
STUDENT NUMBER:
Page 1 of 6
MATH 337 - Test 1
INSTRUCTIONS:
Answer all questions, writing clearly in the space provided. If you need more room, continue your
answer on the back of the page, providing
Introduction To Operations Research Models - MATH 337
Fall 2012
Instructor
Alan Ableson JEFF 505 [email protected]
Course web site: http:/www.mast.queensu.ca/~math337/
Text: No on-paper text. On
MATH 337 - Assignment 3
Due Monday Dec 7 by 4:30 PM to JEFF 505
Assignments may be submitted in groups of up to 3 students.
1. A manager runs several grocery stores. She receives a shipment of strawbe
MATH 337 - Assignment 1
Due Wednesday Oct 21 in class
Assignments may be submitted in groups of up to 3 students.
In this assignment, you are going to extend the camera inventory model seen in class t
MATH 337
Assignment 1 - Solutions
(1) In the steady state, u is independent of t, ie, u = u(x). Therefore, utt = 0, and
our PDE becomes the ODE kuxx = x, with boundary conditions u(0) = 1 and
u(1) = 0
MATH 337
Assignment 3 - Solutions
1) From the derivation in class, the solution is
cn e
u(x, t) =
(2n+1)2
t
4
cos(
n=0
2n + 1
x)
2
where
cn =
2
x cos(
0
2n + 1
x)dx.
2
We use integration by parts to e
MATH 337
Assignment 5 - Solutions
1) Assuming a separable solution, u(r, t) = h(r)g(t), the exact same procedure as in
class leads to
1
h(r) = b sin( r)
r
and
g(t) = cekt
The boundary condition 0 = ur
MATH 337
Assignment 4 - Solutions
1) We look for a separable solution of the form u(x, t) = F (x)G(t). Substituting this
form into the equation yields:
F (x)G (t) = F (x)G(t) + F (x)G(t).
Rearranging
Math 337 - Practice Problems #1
Instructions: These problems are practice for the test problems. You may assume that you will
be provided with:
The formulas for the probability distribution functions