Partial Fraction Decomposition- Problem Set
GE for Math 427k (Fall 2011)
TA : Ryna Karnik
September 1, 2011
For the following expressions (proper rational functions), nd the partial fraction decompositions.
Problem 1
1
x2 1
Problem 2
3
x2 +x2
Problem 3
4x

Differential Equations
Preface
Here are my online notes for my differential equations course that I teach here at Lamar
University. Despite the fact that these are my class notes they should be accessible to anyone
wanting to learn how to solve differenti

Problem Set 2
Linear and Separable First Order Dierential Equations
In problems 1-6, solve the dierential equation or initial value problem.
1. ty + 2y = sin(t)
(Ans. y =
1
t2 [t cos(t)
+ sin(t) + C ])
2. y + y = 5 sin(2t)
(Ans. y = sin(2t) 2 cos(2t) + Ce

GE 207K
Homogeneous Equations
February 1, 2011
This page aims to recap our mini-lecture on homogenous equations.
A dierential equation which can be written in the form
y =g
y
x
.
In other words, the dierential equation can be written such that anywhere th

GE 207K
Eulers Method Overview
February 8, 2010
Overview of Eulers method:
Eulers method is the most basic way of numerically solving ordinary dierential
equations with given intial values.
Lets start out with an Initial Value Problem (IVP) written in the

In problems 1-4, nd the general solution.
1.
dy
dx
3
+ xy =
2.
dy
dt
= 3(y + 2)(y 4).
1
.
x3 (1+x2 )
3. x + 5x 66x = 0.
4. (cos x ln y ) + (1
x
y
dy
+ 2 sin y cos y ) dx = 0 .
5. Solve the initial value problem x 2x + 50x = 0; x(0) = 0, x (0) = 1, to nd

Trigonometric Fourier Series
April 9, 2011
In trigonometric Fourier series, we aim to decompose a periodic function into an (innite)
sum of Sine and Cosine functions.
A function is said to periodic if it repeats itself. Mathematically, a function is perio