Differential Equations: An Introduction to Modern Methods and Applications, 1st Edition

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

• ISBN13: 9780471651413
• ISBN10: 0471651419
• Edition: 1
• Format: Hardcover
• Copyright: 2006-12-01
• Publisher: WILEY

Summary

Differential Equations: An Introduction to Modern Methods and Applications is a textbook designed for a first course in differential equations commonly taken by undergraduates majoring in engineering or science. It emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. Section exercises throughout the text are designed to give students hands-on experience in modeling, analysis, and computer experimentation. Optional projects at the end of each chapter provide additional opportunitites for students to explore the role played by differential equations in scientific and engineering problems of a more serious nature.

Author Biography

William E. Boyce received his B.A. degree in Mathematics from Rhodes College, and his M.S. and Ph.D. degrees in Mathematics from Carnegie-Mellon University. He is a member of the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. He is currently the Edward P. Hamilton Distinguished Professor Emeritus of Science Education (Department of Mathematical Sciences) at Rensselaer. He is the author of numerous technical papers in boundary value problems and random differential equations and their applications. He is the author of several textbooks including two differential equations texts, and is the coauthor (with M.H. Holmes, J.G. Ecker, andW.L. Siegmann) of a text on using Maple to explore Calculus. He is also coauthor (with R.L. Borrelli and C.S. Coleman) of Differential Equations LaboratoryWorkbook (Wiley 1992), which received the EDUCOMBest Mathematics Curricular InnovationAward in 1993. Professor Boyce was a member of the NSF-sponsored CODEE (Consortium for Ordinary Differential Equations Experiments) that led to the widely-acclaimed ODE Architect. He has also been active in curriculum innovation and reform. Among other things, he was the initiator of the "Computers in Calculus" project at Rensselaer, partially supported by the NSF. In 1991 he received the William H.Wiley Distinguished FacultyAward given by Rensselaer.

Table of Contents

Chapter 1. Introduction

Chapter 2. First Order Differential Equations

Chapter 3. Systems of Two First Order Equations

Chapter 4. Second Order Linear Equations

Chapter 5. The Laplace Transform

Chapter 6. Systems of First Order Linear Equations

Chapter 7. Nonlinear Differential Equations and Stability

Appendix A: Matrix Algebra

Appendix B: Complex Variables