MTH 3201 Midterm Test 1: Spring 2010: Solutions
1
First Problem
Solve the heat equation ut = 9uxx for a rod of length with both ends held at zero temperature (zero Dirichlet
boundary conditions) if th
According to the College of Engineering Lab Safety Guide and Chemical Hygiene Plan (see Lab
Reference Manual for how to access this), who may operate a fire extinguisher in the lab, and under what
cir
MTH 3210 Midterm Test 2: Spring 2013 Name: M
1 (25 p ints)
Use Laplace transforms to solve the initial boundary value problem for the wave equation:
utt9u$m=0, 0<$<+oo, 0<t<+oo (1)
u(m,0) = ut(:1:,0
Practice Test 3 - MTH 3210 - Intro to PDE & Apps - Dr. Kanishka
Perera - Spring 2014
1. (30 points) Solve
ut = u, 0 < x < 1, 0 < y < 1, t > 0
u(x, 0, t) = ux (1, y, t) = u(x, 1, t) = ux (0, y, t) = 0
Practice Test 2 - MTH 3210 - Intro to PDE & Apps - Dr. Kanishka Perera Spring 2016
Name:
1. Use the Laplace transform to solve the following initial boundary value problem for
the wave equation:
utt =
Practice Test 2 - MTH 3210 - Intro to PDE & Apps - Dr. Kanishka
Perera - Spring 2014
1. (30 points) Use the Laplace transform to solve
utt = uxx t,
x > 0, t > 0
u(x, 0) = ut (x, 0) = 0,
x>0
ux (0, t)
MTH 3201 Final Exam-E1: Fall 2010: Solutions
1
1
Vibrations in a Rectangular Membrane
Consider the vibrations of the rectangular membrane with two edges fixed and the other two edges
held free.
a. (25
MTH 3201 Final Exam-01: Fall 2013
1
Name:
Vibrations in a Rectangular Membrane
Consider the vibrations of the rectangular membrane with the edges held free.
a. (25 points) Find the general formula for
MTH 3201 Final Exam-01: Fall 2010: Solutions
1
1
Heat Conduction in a Cylinder
Consider Fourier heat conduction in a cylindrical body with a rectangular cross-section. Assume
that the temperature is i
Practice Final Exam - MTH 3210 - Intro to PDE & Apps - Dr.
Kanishka Perera - Spring 2014
1. (a) (65 points) Solve
ut = u, 0 < x < a, 0 < y < b, t > 0
u(x, 0, t) = ux (a, y, t) = u(x, b, t) = ux (0, y,
Homework 13
1
August 8, 2012
9.3
1. a. Calculate in cartesian and polar coordinates that xy = 0.
b.
(2x3 + 3x2 y y 2 ) = 12x + 6y 2
The calculation in polar coordinates, while tedious, yields the same
Homework 13
1
November 15, 2010
9.3
1
a. Calculate in cartesian an polar coordinates that xy = 0. In cartesian coordinates, we
have
2 xy 2 xy
+
x2
y 2
y x
+
=
x y
=0
xy =
In polar coordinates, we wan