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Fundamentals of Differential Equations

by: Nagle, R. Kent; Saff, E. B.; Snider, Arthur David

Fundamentals of Differential Equations

by: Nagle, R. Kent; Saff, E. B.; Snider, Arthur David

ISBN 13:
9780201338683
ISBN 10:
0201338688
Edition: 5th
Format: Hardcover w/CD
Copyright: 01/01/2000
Publisher: Addison Wesley
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Summary

This text is in a flexible one-semester text that spans a variety of topics in the basic theory as well as applications of differential equations.

Introduction

(41)

Background

(5)

Solutions and Initial Value Problems

(10)

Direction Fields

(8)

The Phase Line

(7)

The Approximation Method of Euler

(11)

Chapter Summary

(1)

Technical Writing Exercises

(1)

Group Projects for Chapter 1

(1)

Taylor Series Method

(1)

Picard's Method

(1)

Magnetic Dipole

(2)

First Order Differential Equations

(51)

Introduction: Motion of a Falling Body

(3)

Separable Equations

(9)

Linear Equations

(9)

Exact Equations

(10)

Special Integrating Factors

(4)

Substitutions and Transformations

(16)

Chapter Summary

(1)

Review Problems

(1)

Technical Writing Exercises

(1)

Group Projects for Chapter 2

(1)

The Snowplow Problem

(1)

Two Snowplows

(1)

Asymptotic Behavior of Solutions to Linear Equations

(1)

Torricelli's Law of Fluid Flow

(2)

Clairaut Equations and Singular Solutions

(1)

Mathematical Models and Numerical Methods Involving First Order Equations

(63)

Mathematical Modeling

(2)

Compartmental Analysis

(12)

Heating and Cooling of Buildings

107

(7)

Newtonian Mechanics

114

(10)

Improved Euler's Method

124

(11)

Higher-Order Numerical Methods: Taylor and Runge-Kutta

135

(9)

Professional Codes for Solving Initial Value Problems

144

(12)

Group Projects for Chapter 3

148

(1)

Delay Differential Equations

148

(1)

Aquaculture

149

(1)

Curve of Pursuit

150

(1)

Aircraft Guidance in a Crosswind

151

(1)

Stability of Numerical Methods

152

(1)

Period Doubling and Chaos

153

(2)

Bang-Bang Controls

155

(1)

Linear Second Order Equations

156

(105)

Introduction: The Mass-Spring Oscillator

156

(5)

Linear Differential Operators

161

(7)

Fundamental Solutions of Homogeneous Equations

168

(10)

Reduction of Order

178

(5)

Homogeneous Linear Equations with Constant Coefficients

183

(8)

Auxiliary Equations with Complex Roots

191

(9)

Superposition and Nonhomogeneous Equations

200

(4)

Method of Undetermined Coefficients

204

(9)

Variation of Parameters

213

(5)

Qualitative Considerations for Variable-Coefficient and Nonlinear Equations

218

(12)

A Closer Look at Free Mechanical Vibrations

230

(10)

A Closer Look at Forced Mechanical Vibrations

240

(21)

Chapter Summary

248

(2)

Review Problems

250

(1)

Technical Writing Exercises

251

(1)

Group Projects for Chapter 4

252

(1)

Undetermined Coefficients Using Complex Arithmetic

252

(1)

An Alternative to the Method of Undetermined Coefficients

253

(1)

Convolution Method

254

(1)

Linearization of Nonlinear Problems

255

(1)

Nonlinear Equations Solvable by First Order Techniques

256

(1)

Apollo Reentry

257

(1)

Simple Pendulum

258

(1)

Asymptotic Behavior of Solutions

259

(2)

Introduction to Systems and Phase Plane Analysis

261

(77)

Interconnected Fluid Tanks

261

(2)

Introduction to the Phase Plane

263

(15)

Elimination Method for Systems

278

(8)

Coupled Mass-Spring Systems

286

(7)

Electrical Circuits

293

(8)

Numerical Methods for Higher-Order Equations and Systems

301

(14)

Dynamical Systems, Poincare Maps, and Chaos

315

(23)

Chapter Summary

325

(2)

Review Problems

327

(1)

Group Projects for Chapter 5

328

(1)

Designing a Landing System for Interplanetary Travel

328

(1)

Things That Bob

329

(1)

Effects of Hunting on Predator-Prey Systems

330

(1)

Periodic Solutions to Volterra-Lotka Systems

331

(1)

Hamiltonian Systems

332

(2)

Limit Cycles

334

(1)

Strange Behavior of Competing Species---Part I

335

(1)

Cleaning Up the Great Lakes

336

(2)

Theory of Higher-Order Linear Differential Equations

338

(31)

Basic Theory of Linear Differential Equations

338

(9)

Homogeneous Linear Equations with Constant Coefficients

347

(7)

Undetermined Coefficients and the Annihilator Method

354

(6)

Method of Variation of Parameters

360

(9)

Chapter Summary

364

(2)

Review Problems

366

(1)

Technical Writing Exercises

366

(1)

Group Projects for Chapter 6

367

(1)

Justifying the Method of Undetermined Coefficients

367

(1)

Transverse Vibrations of Beam

367

(2)

Laplace Transforms

369

(78)

Introduction: A Mixing Problem

369

(4)

Definition of the Laplace Transform

373

(9)

Properties of the Laplace Transform

382

(6)

Inverse Laplace Transform

388

(10)

Solving Initial Value Problems

398

(8)

Transforms of Discontinuous and Periodic Functions

406

(14)

Convolution

420

(9)

Impulses and the Dirac Delta Function

429

(7)

Solving Linear Systems with Laplace Transforms

436

(11)

Chapter Summary

439

(1)

Review Problems

440

(1)

Technical Writing Exercises

441

(2)

Group Projects for Chapter 7

443

(1)

Duhamel's Formulas

443

(1)

Frequency Response Modeling

444

(2)

Determining System Parameters

446

(1)

Series Solutions of Differential Equations

447

(80)

Introduction: The Taylor Polynomial Approximation

447

(6)

Power Series and Analytic Functions

453

(9)

Power Series Solutions to Linear Differential Equations

462

(11)

Equations with Analytic Coefficients

473

(6)

Cauchy-Euler (Equidimensional) Equations Revisited

479

(4)

Method of Frobenius

483

(12)

Finding a Second Linearly Independent Solution

495

(12)

Special Functions

507

(20)

Chapter Summary

520

(1)

Review Problems

521

(1)

Technical Writing Exercises

522

(1)

Group Projects for Chapter 8

523

(1)

Spherically Symmetric Solutions to Schrodinger's Equation for the Hydrogen Atom

523

(1)

Airy's Equation

524

(1)

Buckling of a Tower

524

(1)

Aging Spring and Bessel Functions

525

(2)

Matrix Methods for Linear Systems

527

(73)

Introduction

527

(5)

Linear Algebraic Equations

532

(4)

Matrices and Vectors

536

(12)

Linear Systems in Normal Form

548

(9)

Homogeneous Linear Systems with Constant Coefficients

557

(12)

Complex Eigenvalues

569

(6)

Nonhomogeneous Linear Systems

575

(7)

The Matrix Exponential Function

582

(18)

Chapter Summary

591

(3)

Review Problems

594

(1)

Technical Writing Exercises

595

(1)

Group Projects for Chapter 9

596

(1)

Uncoupling Normal Systems

596

(1)

Matrix Laplace Transform Method

596

(2)

Undamped Second Order Systems

598

(1)

Strange Behavior of Competing Species---Part II

599

(1)

Partial Differential Equations

600

Introduction: A Model for Heat Flow

600

(3)

Method of Separation of Variables

603

(10)

Fourier Series

613

(18)

Fourier Cosine and Sine Series

631

(5)

The Heat Equation

636

(13)

The Wave Equation

649

(13)

Laplace's Equation

662

Chapter Summary

675

(2)

Technical Writing Exercises

677

(1)

Group Projects for Chapter 10

678

(1)

Steady-State Temperature Distribution in a Circular Cylinder

678

(1)

A Laplace Transform Solution of the Wave Equation

679

(1)

Green's Function

680

(2)

Numerical Method for Δu = f on a Rectangle

682

APPENDICES

A-1

(1)

A. Newton's Method

A-1

(1)

B. Simpson's Rule

A-3

(1)

C. Cramer's Rule

A-5

(1)

D. Method of Least Squares

A-6

(1)

E. Runge-Kutta Procedure for n Equations

A-9

(1)

Answers to Odd-Numbered Problems

B-1

(1)

Index

I-1

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Fundamentals of Differential Equations

Fundamentals of Differential Equations

9780201338683

0201338688

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Fundamentals of Differential Equations

Fundamentals of Differential Equations

9780201338683

0201338688

Summary

Table of Contents

Supplemental Materials

Write a Review

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