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Elementary Differential Equations with Boundary Value Problems

Elementary Differential Equations with Boundary Value Problems - 6th edition

ISBN13: 978-0136006138

Cover of Elementary Differential Equations with Boundary Value Problems 6TH 08 (ISBN 978-0136006138)
ISBN13: 978-0136006138
ISBN10: 0136006132
Cover type: Hardback
Edition/Copyright: 6TH 08
Publisher: Prentice Hall, Inc.
Published: 2008
International: No
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Elementary Differential Equations with Boundary Value Problems - 6TH 08 edition

ISBN13: 978-0136006138

Henry Edwards and David Penney

ISBN13: 978-0136006138
ISBN10: 0136006132
Cover type: Hardback
Edition/Copyright: 6TH 08
Publisher: Prentice Hall, Inc.

Published: 2008
International: No
Summary

This book enables readers to first solve those differential equations that have the most frequent and interesting applications. This approach illustrates the standard elementary techniques of solution of differential equations. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques.The first few sections of most chapters introduce the principle ideas of each topic, with remaining sections devoted to extensions and applications. Topics covered include first-order differential equations, linear equations of higher order, power series methods, Laplace transform methods, linear systems of differential equations, numerical methods, nonlinear systems and phenomena, Fourier series methods, and Eigenvalues and boundary value problems.For those involved in the fields of science, engineering, and mathematics.

Table of Contents

Preface

1 First-Order Differential Equations 1.1 Differential Equations and Mathematical Models 1.2 Integrals as General and Particular Solutions 1.3 Slope Fields and Solution Curves 1.4 Separable Equations and Applications 1.5 Linear First-Order Equations 1.6 Substitution Methods and Exact Equations 1.7 Population Models 1.8 Acceleration-Velocity Models

2 Linear Equations of Higher Order 2.1 Introduction: Second-Order Linear Equations 2.2 General Solutions of Linear Equations 2.3 Homogeneous Equations with Constant Coefficients 2.4 Mechanical Vibrations 2.5 Nonhomogeneous Equations and Undetermined Coefficients 2.6 Forced Oscillations and Resonance 2.7 Electrical Circuits 2.8 Endpoint Problems and Eigenvalues

3 Power Series Methods 3.1 Introduction and Review of Power Series 3.2 Series Solutions Near Ordinary Points 3.3 Regular Singular Points 3.4 Method of Frobenius: The Exceptional Cases 3.5 Bessel's Equation 3.6 Applications of Bessel Functions

4 LaplaceTransform Methods 4.1 Laplace Transforms and Inverse Transforms 4.2 Transformation of Initial Value Problems 4.3 Translation and Partial Fractions 4.4 Derivatives, Integrals, and Products of Transforms 4.5 Periodic and Piecewise Continuous Input Functions 4.6 Impulses and Delta Functions

5 Linear Systems of Differential Equations 5.1 First-Order Systems and Applications 5.2 The Method of Elimination 5.3 Matrices and Linear Systems 5.4 The Eigenvalue Method for Homogeneous Systems 5.5 Second-Order Systems and Mechanical Applications 5.6 Multiple Eigenvalue Solutions 5.7 Matrix Exponentials and Linear Systems 5.8 Nonhomogeneous Linear Systems

6 Numerical Methods 6.1 Numerical Approximation: Euler's Method 6.2 A Closer Look at the Euler Method 6.3 The Runge-Kutta Method 6.4 Numerical Methods for Systems

7 Nonlinear Systems and Phenomena 7.1 Equilibrium Solutions and Stability 7.2 Stability and the Phase Plane 7.3 Linear and Almost Linear Systems 7.4 Ecological Models: Predators and Competitors 7.5 Nonlinear Mechanical Systems 7.6 Chaos in Dynamical Systems 8Fourier Series Methods 8.1 Periodic Functions and Trigonometric

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