MAT 432 - SPRING 2013
Project 1
Ryan Szypowski
Due May 16, 2013
Instructions
In this project, you will solve for the steady-state heat distribution in a cube. The mathematical details are given below.
The deliverable for the project should be a written re
MAT 432 - SPRING 2013
Project 2
Ryan Szypowski
Due June 13, 2013
Instructions
In this project, you will solve for a conserved quantity related to water ow through a porous
medium.
The deliverable for the project should be a written report in which you dev
MAT 432 - Spring 2013
Homework 4 Solutions
Ryan Szypowski
Due June 6, 2013
1. Find the solution to the following wave equation:
utt = c2 uxx for 0 < x < 1, t > 0,
u(0, t) = ux (1, t) = 0,
u(x, 0) = f (x),
ut (x, 0) = 0.
Solution: We begin by separation of
MAT 432 - Spring 2013
Homework 4
Ryan Szypowski
Due June 6, 2013
1. Find the solution to the following wave equation:
utt = c2 uxx for 0 < x < 1, t > 0,
u(0, t) = ux (1, t) = 0,
u(x, 0) = f (x),
ut (x, 0) = 0.
2. Find the solution to the following rst-ord
MAT 432 SPRING 2013
Name:
Test
Please show all of your work. Answers without justifaction may be worth 0.
Please make your answers easy to read. This means it should be clear what you are doing
from one step to the next and your work should be legible.
1)
MAT 432 - Spring 2013
Homework 2 Solution
Ryan Szypowski
Due April 30, 2013
1. Find all eigenvalues and the corresponding eigenfunctions for the following SturmLouisville problem
u (x) = u(x),
u(0) = 0,
u (1) = 0.
Solution: We break this into cases as bel
MAT 432 - Spring 2013
Homework 1
Ryan Szypowski
Due April 18, 2013
1. Dene the following functions where m is an arbitrary integer:
u1 (x, t)
u2 (x, t)
u3 (x, t)
u4 (x, t)
u5 (x, t)
=
=
=
=
=
sin(mt) sin(mx)
exp(m)2 t) sin(mx)
cos(mt) cos(mx)
1
exp(m + 1
MAT 432 - Spring 2013
Homework 1
Ryan Szypowski
Due April 18, 2013
1. Dene the following functions where m is an arbitrary integer:
u1 (x, t)
u2 (x, t)
u3 (x, t)
u4 (x, t)
u5 (x, t)
=
=
=
=
=
sin(mt) sin(mx)
exp(m)2 t) sin(mx)
cos(mt) cos(mx)
1
exp(m + 1
MAT 432 - Spring 2013
Homework 3
Ryan Szypowski
Due May 23, 2013
1. Find the solution to the following heat equation with Dirichlet boundary conditions:
ut = Duxx for 0 < x < 1, t > 0,
u(0, t) = u(1, t) = 0,
u(x, 0) = f (x).
2. Find the solution to the fo
MAT 432 - Spring 2013
Homework 2
Ryan Szypowski
Due April 30, 2013
1. Find all eigenvalues and the corresponding eigenfunctions for the following SturmLouisville problem
u (x) = u(x),
u(0) = 0,
u (1) = 0.
2. Under what conditions on the parameter does the