Ordinary Differential Equations

Charles E. Roberts, Jr. is a professor in the Department of Mathematics and Computer Science at Indiana State University.

Introduction
Historical Prologue
Definitions and Terminology
Solutions and Problems
A Nobel Prize Winning Application


The Initial Value Problem y′ = f (x, y); y(c) =d
Direction Fields
Fundamental Theorems
Solution of Simple First-Order Differential Equations
Numerical Solution


Applications of the Initial Value Problem y′ = f (x, y); y(c) =d
Calculus Revisited
Learning Theory Models
Population Models
Simple Epidemic Models
Falling Bodies
Mixture Problems
Curves of Pursuit
Chemical Reactions


N-th Order Linear Differential Equations
Basic Theory
Roots of Polynomials
Homogeneous Linear Equations with Constant Coefficients
Nonhomogeneous Linear Equations with Constant Coefficients
Initial Value Problems


The Laplace Transform Method
The Laplace Transform and Its Properties
Using the Laplace Transform and Its Inverse to Solve Initial Value Problems
Convolution and the Laplace Transform
The Unit Function and Time-Delay Functions
Impulse Functions


Applications of Linear Differential Equations with Constant Coefficients
Second-Order Differential Equations
Higher Order Differential Equations


Systems of First-Order Differential Equations


Linear Systems of First-Order Differential Equations
Matrices and Vectors
Eigenvalues and Eigenvectors
Linear Systems with Constant Coefficients


Applications of Linear Systems with Constant Coefficients
Coupled Spring-Mass Systems
Pendulum Systems
The Path of an Electron
Mixture Problems


Applications of Systems of Equations
Richardson’s Arms Race Model
Phase-Plane Portraits
Modified Richardson’s Arms Race Models
Lanchester’s Combat Models
Models for Interacting Species
Epidemics
Pendulums
Duffing’s Equation
Van der Pol’s Equation
Mixture Problems
The Restricted Three-Body Problem


Appendix A: CSODE User’s Guide
Appendix B: PORTRAIT User’s Guide
Appendix C: Laplace Transforms





Answers to Selected Exercises


References


Index