Book Description
The modern landscape of technology and industry demands an equally modern approach to differential equations in the classroom. Designed for a first course in differential equations, the second edition of Brannan/Boyce's Differential Equations: An Introduction to Modern Methods and Applications is consistent with the way engineers and scientists use mathematics in their daily work. The focus on fundamental skills, careful application of technology, and practice in modeling complex systems prepares students for the realities of the new millennium, providing the building blocks to be successful problemsolvers in today's workplace.
The text 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 provide handson experience in modeling, analysis, and computer experimentation. Projects at the end of each chapter provide additional opportunities for students to explore the role played by differential equations in the sciences and engineering.
Brannan/Boyce's Differential Equations 2e is available with WileyPLUS, an online teaching and learning environment initially developed for Calculus and Differential Equations courses. WileyPLUS integrates the complete digital textbook, incorporating robust student and instructor resources with online autograded homework to create a singular online learning suite so powerful and effective that no course is complete without it.
Table of Contents
 Coverpage
 Titlepage
 Copyright
 Preface
 Contents
 1 Introduction
 2 First Order Differential Equations

3 Systems of Two First Order Equations
 3.1 Systems of Two Linear Algebraic Equations
 3.2 Systems of Two First Order Linear Differential Equations
 3.3 Homogeneous Linear Systems with Constant Coefficients
 3.4 Complex Eigenvalues
 3.5 Repeated Eigenvalues
 3.6 A Brief Introduction to Nonlinear Systems
 3.7 Numerical Methods for Systems of First Order Equations
 Projects

4 Second Order Linear Equations
 4.1 Definitions and Examples
 4.2 Theory of Second Order Linear Homogeneous Equations
 4.3 Linear Homogeneous Equations with Constant Coefficients
 4.4 Mechanical and Electrical Vibrations
 4.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
 4.6 Forced Vibrations, Frequency Response, and Resonance
 4.7 Variation of Parameters
 Projects

5 The Laplace Transform
 5.1 Definition of the Laplace Transform
 5.2 Properties of the Laplace Transform
 5.3 The Inverse Laplace Transform
 5.4 Solving Differential Equations with Laplace Transforms
 5.5 Discontinuous Functions and Periodic Functions
 5.6 Differential Equations with Discontinuous Forcing Functions
 5.7 Impulse Functions
 5.8 Convolution Integrals and Their Applications
 5.9 Linear Systems and Feedback Control
 Projects

6 Systems of First Order Linear Equations
 6.1 Definitions and Examples
 6.2 Basic Theory of First Order Linear Systems
 6.3 Homogeneous Linear Systems with Constant Coefficients
 6.4 Nondefective Matrices with Complex Eigenvalues
 6.5 Fundamental Matrices and the Exponential of a Matrix
 6.6 Nonhomogeneous Linear Systems
 6.7 Defective Matrices
 Projects
 7 Nonlinear Differential Equations and Stability
 A Matrices and Linear Algebra
 B Complex Variables
 Answers to Selected Problems
 References
 Photo Credits
 Index
Product Information
 Title: Differential Equations: An Introduction to Modern Methods and Applications, 2nd Edition
 Author(s):
 Release date: December 2010
 Publisher(s): Wiley
 ISBN: 9780470458242