Differential Equations With Boundary Value Problems: An Introduction to Modern Methods and Applications

by James R. Brannan (Clemson University); William E. Boyce (Rensselaer Polytechnic Institute)

• ISBN13: 9780470418505
• ISBN10: 0470418508
• Edition: 1
• Format: Hardcover
• Copyright: 2009-04-01
• Publisher: Wiley

Summary

Brannan provides engineers with both an introduction to, and a survey of, modern methods, applications, and theory of a powerful mathematical apparatus that will help them in the field. Section exercises of varying levels of difficulty give them hands-on experience in modeling, analysis, and computer experimentation. New coverage is included on series solutions of second order linear equations, partial differential equations and Fourier Solutions, and boundary value problems and Sturm-Liouville Theory. The companion ODE Architect CD arms them with a user-friendly software tool for computing numerical approximations to solutions of systems of differential equations, and for constructing component plots, direction fields, and phase portraits. Physical representations of dynamical systems and animations available in the ODE Architect enable engineers to visualize solutions routinely.

Table of Contents

Introduction

First Order Differential Equations

Systems of Two First Order Equations

Second Order Linear Equations

The LaPlace Transform

Systems of First Order Linear Equations

Nonlinear Differential Equations and Stability

Series Solutions of Second Order Linear Equations

Partial Differential Equations and Fourier Series

Boundary Value Problems and Sturm-Liouville Theory

Matrices and Linear Algebra

Complex Variables

Answers to Selected Problems

References

Index

Table of Contents provided by Publisher. All Rights Reserved.