Catalog Description: ORDINARY & PARTIAL DIFFERENTIAL EQUATIONS (4) First and second order equations; special functions; Laplace transform solutions; higher order equations; Fourier; series; partial differential equations.

Prerequisite: Math 141

Text: Elementary Differential Eqns with Boundary Value Problems, Edwards and Penney, Prentice Hall

CHAPTER 1 INTRODUCTION AND FIRST ORDER DIFFERENTIAL EQUATIONS
1.1  Introduction
1.2  Solution by Direct Integration
1.3  Existence and Uniqueness of Solutions
1.4  Separable Equations and Applications
1.5  Linear First Order Equations 
1.7  Exact Equations and Integrating Factors
1.9  Motion with Variable Acceleration

CHAPTER 2 LINEAR EQUATIONS OF HIGHER ORDER
2.1  Introduction
2.2  General Solutions of Linear Equations
2.3  Homogeneous Equations with Constant Coefficients
2.4  Mechanical Vibrations
2.5  Nonhomogeneous Equations and The Method of Undetermined Coefficients
2.7  Variation of Parameters
2.8  Forced Oscillations
2.9  Electrical Circuits

CHAPTER 3  POWER SERIES SOLUTIONS OF HIGHER ORDER
3.2  Series Solutions near Ordinary Points
3.3  Regular Singular Points

CHAPTER 4  THE LAPLACE TRANSFORM
4.1  Laplace Transforms and Inverse Transforms
4.2  Transformation of Initial Value Problems
4.3  Translation and Partial Fractions
4.5  Periodic and Piecewise Continuous Forcing Functions
4.6  Impulses and The Delta Function

CHAPTER 5  LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS
5.1  Introduction to Systems
5.2  The Method of Elimination
5.5  The Eigenvalue Method for Homogeneous Systems

CHAPTER 8  FOURIER SERIES AND SEPARATION OF VARIABLES
8.1  Periodic Functions and Trigonometric Series
8.2  General Fourier Series and Convergence
8.3  Even and Odd Functions and Termwise Differentiation
8.5  Heat Conduction and Separation of Variables
8.6  Vibrating String and The One-Dimensional Wave Equation
8.7  Steady State Temperature and Laplace's Equation