Ordinary Differential Equations: Applications, Models, and Computing

Ordinary Differential Equations: Applications, Models, and Computing

by Charles Roberts

Paperback

$75.95 $79.95 Save 5% Current price is $75.95, Original price is $79.95. You Save 5%.
Choose Expedited Shipping at checkout for guaranteed delivery by Friday, March 22

Product Details

ISBN-13: 9781138118218
Publisher: Taylor & Francis
Publication date: 07/02/2018
Series: Textbooks in Mathematics Series
Pages: 600
Product dimensions: 8.26(w) x 11.68(h) x (d)

About the Author

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

Table of Contents

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

What People are Saying About This

From the Publisher

Roberts gives a clear, detailed introduction to ordinary differential equations for students who have completed the full calculus sequence. … the book’s exercises and examples … are independent of any particular software—a very nice feature. Roberts provides a good balance between theoretical and applied material. … The work is very readable and offers instructors much material to work with in their courses. Summing Up: Recommended.
CHOICE, December 2010

Customer Reviews

Most Helpful Customer Reviews

See All Customer Reviews