Differential Equations

Syllabus Fall 09

Schedule of Classes

If you did not take Multivariable Calculus, you need to learn the rudiments of Partial Derivatives

Partial Derivatives

Chapter 1

Introduction to Differential Equations

Solutions of Differential Equations

Homework

Classify Differential Equations by Order and Degree

Answer Key to Classify

Theorem on Existence

Answer Key to Theorem on Existence

Chapter 2

Introduction to First Order Differential Equations

Exact Equations

Integrating Factors

Separable Equations

Homogeneous Equations

Linear Equations

Special Integrating Factors

Special Transformations

Summary of First Order Differential Equations

Homework

Classify First Order O.D.E.

Answer Key First Order O.D.E

Classify and Solve First Order O.D.E

Answer Key Classify and Solve

Chapter 3

Modeling First Order O.D.E.

Chapter 4

Preparation for Chapter 4

Basic Theory of n-th Order Linear Differential Equations

Method of Reduction of Order

Homogeneous Linear D.E. with Constant Coefficients

The Method of Undetermined Coefficients

Variation of Parameters

The Cauchy-Euler Equation

Homework

Problems on Linear Differential Equations

Answer Key Problems on Linear Equations

Chapter 9

Improper Integrals

Introduction to the Laplace Transform

Properties of the Laplace Transform

Step Functions

Inverse Laplace Transform

Application of the Laplace Transform to Linear Differential Equations

Homework

Laplace Transform Exercises

Answer Key Laplace Transform Exercises

Table of Laplace Transforms

Chapter 6

Introduction and Review of Power Series

Series Solutions Near an Ordinary Point

Regular Singular Points-The Method of Frobenius

Homework

Solve non-Homogeneous Equations by Power Series Method