Differential Equations : Computing and Modeling,9780133821024

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Differential Equations : Computing and Modeling

by Edwards, C.h.

ISBN13:

9780133821024

ISBN10:

0133821021

Format:

Hardcover

Pub. Date:

6/1/1996

Publisher(s):

PRENTICE HALL

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Summary

Textbook of differential equations. Author's approach reflects the widespread use of new computer methods for the solution of differential equations. DLC: Differential equations.

Preface

1 First-Order Differential Equations

(68)

1.1 Differential Equations and Mathematical Models

(9)

1.2 Integrals as General and Particular Solutions

(7)

1.3 Slope Fields and Solution Curves

(10)

1.4 Separable Equations and Applications

(14)

1.5 Linear First-Order Equations

(11)

1.6 Substitution Methods and Exact Equations

(13)

Chapter 1 Summary

(4)

2 Mathematical Models and Numerical Methods

(60)

2.1 Population Models

(11)

2.2 Equilibrium Solutions and Stability

(6)

2.3 Acceleration-Velocity Models

(13)

2.4 Numerical Approximation: Euler's Method

(9)

2.5 A Closer Look at the Euler Method

105

(12)

2.6 The Runge-Kutta Method

117

(12)

3 Linear Equations of Higher Order

129

(90)

3.1 Introduction: Second-Order Linear Equations

129

(12)

3.2 General Solutions of Linear Equations

141

(11)

3.3 Homogeneous Equations with Constant Coefficients

152

(11)

3.4 Mechanical Vibrations

163

(10)

3.5 Nonhomogeneous Equations and the Methods of Undetermined Coefficients

173

(14)

*3.6 Forced Oscillations and Resonance

187

(11)

*3.7 Electrical Circuits

198

(7)

*3.8 Endpoint Problems and Eigenvalues

205

(14)

4 Introduction to Systems of Differential Equations

219

(36)

4.1 First-Order Systems and Applications

219

(10)

4.2 The Method of Elimination

229

(11)

4.3 Numerical Methods for Systems

240

(15)

5 Linear Systems of Differential Equations

255

(78)

5.1 Matrices and Linear Systems

255

(21)

5.2 The Eigenvalue Method for Homogeneous Systems

276

(15)

*5.3 Second-Order Systems and Mechanical Applications

291

(13)

5.4 Multiple Eigenvalue Solutions

304

(16)

*5.5 Matrix Exponentials and Linear Systems

320

(13)

6 Nonlinear Systems and Phenomena

333

(64)

6.1 Stability and the Phase Plane

333

(12)

6.2 Liear and Almost Linear Systems

345

(13)

6.3 Ecological Applications: Predators and Competitors

358

(11)

6.4 Nonlinear Mechanical Systems

369

(14)

6.5 Chaos in Dynamical Systems

383

(14)

7 Laplace Transform Methods

397

(60)

7.1 Laplace Transforms and Inverse Transforms

397

(11)

7.2 Transformation of Initial Value Problems

408

(10)

7.3 Translation and Partial Fractions

418

(9)

7.4 Derivatives, Integrals, and Products of Transforms

427

(8)

*7.5 Periodic and Piecewise Continuous Input Functions

435

(12)

7.6 Impulses and Delta Functions

447

(10)

References for Further Study

457

(4)

Appendix

461

(16)

Answers to Selected Problems

477

Index

I-1

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Differential Equations : Computing and Modeling

9780133821024

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