Catalog Description: ORDINARY DIFFERENTIAL EQUATIONS (3) First and second order equations; numerical methods; special functions; Laplace transform solutions; higher order equations. (Students who have passed Math 251 may not schedule this course).

Prerequisite: Math 141

Text: Elementary Differential Eqns with Boundary Value Problems, Edwards & 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 (OPTIONAL)

CHAPTER 3 POWER SERIES SOLUTIONS OF LINEAR EQUATIONS
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
=====OR====
CHAPTER 6 NUMERICAL METHODS
6.1  Introduction: Euler's Method
6.2  A Closer Look at Euler Method and Improvements
6.3  The Runge-Kutta Method