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

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

• ISBN13: 9780470125533
• ISBN10: 0470125535
• Edition: Student
• Format: Paperback
• Copyright: 2007-02-01
• Publisher: Wiley

Summary

Written by one of the most well known names in mathematics, this book provides readers with a more modern approach to differential equations. It is streamlined for easier readability while incorporating the latest topics and technologies. The modeling- and technology-intensive format allows readers who may normally struggle with learning the subject to feel confident. It also incorporates numerous exercises that have been developed and tested over decades.

Table of Contents

Introduction	p. 1
Some Basic Mathematical Models; Direction Fields	p. 1
Solutions of Some Differential Equations	p. 5
Numerical Approximations: Euler's Method	p. 12
Classification of Differential Equations	p. 15
First Order Differential Equations	p. 1
Linear Equations; Method of Integrating Factors	p. 1
Separable Equations	p. 8
Modeling with First Order Equations	p. 16
Differences Between Linear and Nonlinear Equations	p. 26
Autonomous Equations and Population Dynamics	p. 44
Exact Equations and Integrating Factors	p. 38
Accuracy of Numerical Methods	p. 44
Improved Euler and Runge-Kutta Methods	p. 48
Systems of Two First Order Equations	p. 1
Systems of Two Linear Algebraic Equations	p. 1
Systems of Two First Order Linear Differential Equations	p. 8
Homogeneous Linear Systems with Constant Coefficients	p. 13
Complex Eigenvalues	p. 29
Repeated Eigenvalues	p. 38
A Brief Introduction to Nonlinear Systems	p. 45
Numerical Methods for Systems of First Order Equations	p. 55
Second Order Linear Equations	p. 1
Definitions and Examples	p. 1
Theory of Second Order Linear Homogeneous Equations	p. 4
Linear Homogeneous Equations with Constant Coefficients	p. 5
Characteristic Equations with Complex Roots	p. 17
Mechanical and Electrical Vibrations	p. 29
Nonhomogeneous Equations; Method of Undetermined Coefficients	p. 38
Forced Vibrations, Frequency Response, and Resonance	p. 45
Variation of Parameters	p. 51
The Laplace Transform	p. 1
Definition of the Laplace Transform	p. 1
Properties of the Laplace Transform	p. 7
The Inverse Laplace Transform	p. 13
Solving Differential Equations with Laplace Transforms	p. 16
Discontinuous Functions and Periodic Functions	p. 26
Differential Equations with Discontinuous Forcing Functions	p. 31
Impulse Functions	p. 43
Convolution Integrals and Their Applications	p. 52
Linear Systems and Feedback Control	p. 61
Systems of First Order Linear Equations	p. 1
Definitions and Examples	p. 1
Basic Theory of First Order Linear Systems	p. 5
Homogeneous Linear Systems with Constant Coefficients	p. 7
Complex Eigenvalues	p. 22
Fundamental Matrices and the Exponential of a Matrix	p. 33
Nonhomogeneous Linear Systems	p. 40
Defective Matrices	p. 47
Nonlinear Differential Equations and Stability	p. 1
Autonomous Systems and Stability	p. 1
Almost Linear Systems	p. 7
Competing Species	p. 23
Predator-Prey Equations	p. 36
Periodic Solutions and Limit Cycles	p. 45
Chaos and Strange Attractors: The Lorenz Equations	p. 56
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