The CLASSIC EDITION of Zill's respected book was designed for instructors who prefer not to emphasize technology, modeling, and applications, but instead want to focus on fundamental theory and techniques. Zill's CLASSIC EDITION, a reissue of the fifth edition, offers his excellent writing style, a flexible organization, an accessible level of presentation, and a wide variety of examples and exercises, all of which make it easy to teach from and easy for readers to understand and use.

A Word from the Publisher

ix

Preface to the Fifth Edition

xi

Introduction to Differential Equations

1

(27)

Basic Definitions and Terminology

2

(9)

Some Mathematical Models

11

(17)

Review

25

(1)

Review Exercises

26

(2)

First-Order Differential Equations

28

(47)

Preliminary Theory

29

(4)

Separable Variables

33

(7)

Homogeneous Equations

40

(6)

Exact Equations

46

(8)

Linear Equations

54

(8)

Equations of Bernoulli, Ricatti, and Clairaut

62

(5)

Substitutions

67

(3)

Picard's Method

70

(5)

Review

72

(1)

Review Exercises

73

(2)

Applications of First-Order Differential Equations

75

(36)

Orthogonal Trajectories

76

(5)

Applications of Linear Equations

81

(12)

Applications of Nonlinear Equations

93

(18)

Review

103

(1)

Review Exercises

104

(2)

Essay: Population Dynamics

106

(5)

Michael Olinick

Linear Differential Equations of Higher-Order

111

(72)

Preliminary Theory

112

(21)

Initial-Value and Boundary-Value Problems

112

(3)

Linear Dependence and Linear Independence

115

(5)

Solutions of Linear Equations

120

(13)

Constructing a Second Solution from a Known Solution

133

(5)

Homogeneous Linear Equations with Constant Coefficients

138

(8)

Undetermined Coefficients-Superposition Approach

146

(11)

Differential Operators

157

(5)

Undetermined Coefficient---Annihilator Approach

162

(7)

Variation of Parameters

169

(14)

Review

175

(2)

Review Exercises

177

(2)

Essay: Chaos

179

(4)

John H. Hubbard

Applications of Second-Order Differential Equations: Vibrational Models

183

(38)

Simple Harmonic Motion

184

(8)

Damped Motion

192

(8)

Forced Motion

200

(9)

Electric Circuits and Other Analogous Systems

209

(12)

Review

214

(1)

Review Exercises

215

(3)

Essay: Tacoma Narrows Suspension Bridge Collapse

218

(3)

Gilbert N. Lewis

Differential Equations with Variable Coefficients

221

(59)

Cauchy-Euler Equation

222

(8)

Review of Power Series; Power Series Solutions

230

(9)

Solutions About Ordinary Points

239

(9)

Solutions About Singular Points

248

(17)

Regular Singular Points; Method of Frobenius---Case I

248

(9)

Method of Frobenius---Cases II and III

257

(8)

Two Special Equations

265

(15)

Solution of Bessel's Equation

266

(5)

Solution of Legendre's Equation

271

(6)

Review

277

(1)

Review Exercises

278

(2)

Laplace Transform

280

(55)

Laplace Transform

281

(9)

Inverse Transform

290

(6)

Translation Theorems and Derivatives of a Transform

296

(11)

Transforms of Derivatives, Integrals, and Periodic Functions

307

(7)

Applications

314

(14)

Dirac Delta Function

328

(7)

Review

332

(1)

Review Exercises

332

(3)

Systems of Linear Differential Equations

335

(86)

Operator Method

336

(7)

Laplace Transform Method

343

(7)

Systems of Linear First-Order Equations

350

(5)

Introduction to Matrices

355

(20)

Basic Definitions and Theory

355

(9)

Gaussian and Gauss-Jordan Elimination Methods

364

(4)

The Eigenvalue Problem

368

(7)

Matrices and Systems of Linear First-Order Equations

375

(16)

Preliminary Theory

375

(9)

A Fundamental Matrix

384

(7)

Homogeneous Linear Systems

391

(14)

Distinct Real Eigenvalues

391

(3)

Complex Eigenvalues

394

(4)

Repeated Eigenvalues

398

(7)

Undetermined Coefficients

405

(4)

Variation of Parameters

409

(4)

Matrix Exponential

413

(8)

Review

416

(2)

Review Exercises

418

(3)

Numerical Methods for Ordinary Differential Equations

421

(1)

Direction Fields

422

(4)

The Euler Methods

426

(6)

The Three-Term Taylor Method

432

(3)

The Runge-Kutta Method

435

(4)

Multistep Methods

439

(3)

Errors and Stability

442

(6)

Higher-Order Equations and Systems

448

(4)

Second-Order Boundary-Value Problems

452

(4)

Review

456

(1)

Review Exercises

457

(2)

Essay: Nerve Impulse Models

459

C. J. Knickerbocker

APPENDIXES

I Gamma Function

1

(3)

II Laplace Transforms

4

(3)

III Review of Determinants

7

(4)

IV Complex Numbers

11

Answers to Odd-Numbered Problems

1

(1)

Index

1

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A First Course in Differential Equations The Classic Fifth Edition

9780534373887

0534373887

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