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 + 1)x) + sin(n 1)x)]dx
0
1 cos(n + 1)x) cos(n 1)x)
=
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, and
If long sums are required for a cumulative distr
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, and
If long sums are required for a cumulative distr
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 functions we have covered in class, and
If long sums
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 Reference sheet, and
If long sums are required for a cumula
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 clear directions to the marker.
Show all your work an
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 clear directions to the marker.
Show all your work an
Introduction To Operations Research Models - MATH 337
Fall 2012
Instructor
Alan Ableson JEFF 505 ableson@mast.queensu.ca
Course web site: http:/www.mast.queensu.ca/~math337/
Text: No on-paper text. Online resources will be used.
For those wanting access t
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 strawberries.
The strawberries will last a week on the store
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 to compare dierent
stocking strategies. We will also inc
Excel Reference
For Assignment #3
Poisson:
=POISSON(2, 5, 0) = P (d = 2|mean = 5)
=POISSON(2, 5, 1) = P (d 2|mean = 5)
=1-POISSON(1, 5, 1) = P (d 2|mean = 5)
Cell coordinates: to x the row, column, or both of a cell coordinate in a formula, use dollar s
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. We can solve this by integrating directly. We obtain:
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 evaluate the integral. Setting u = x, so that du = dx an
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 (, t) = h ()g(t) yields either g(t) = 0 which leads to
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 yields:
G (t)
F (x)
=
+ 1.
G(t)
F (x)
As usual, we conc
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 we have covered in class, and
If long sums are requir