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Elementary Differential Equations, 6/E
C. Henry Edwards
David E. Penney, University of Georgia, Athens

ISBN-10: 0132397307
ISBN-13:  9780132397308

Publisher:  Pearson
Copyright:  2008
Format:  Cloth; 648 pp
Published:  11/28/2007
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Description

For briefer traditional courses in elementary differential equations that science, engineering, and mathematics students take following calculus.

 

The Sixth Edition of this widely adopted book remains the same classic differential equations text it's always been, but has been polished and sharpened to serve both instructors and students even more effectively.Edwards and Penney teach students to first solve those differential equations that have the most frequent and interesting applications. 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.

 


Features

• A solid numerical emphasis – Includes generic numerical algorithms and a limited number of illustrative graphic calculator, BASIC, and MATLAB routines.

 

• Wide range of choices regarding breadth and depth of coverage – The first few sections of most chapters introduce the principal ideas of each topic, with remaining sections devoted to extensions and applications.

 

• Computer-generated figures – Includes graphics using Mathematica or MATLAB; shows students vivid pictures of direction fields, solution curves, and phase plane portraits that bring symbolic solutions of differential equations to life.

 

• Application Modules – Follow appropriate sections in the book; give students concrete applied emphasis and engages them in more extensive investigations than in typical exercises and problems.

 

• Instructor's Solutions Manual – Provides worked-out solutions for most of the problems in the book.

 

• Student Solutions Manual – Contains solutions for most of the odd-numbered problems.

 

 • Proven chapter and section structure of the book is unchanged – Instructors' notes and syllabi will not require revision to continue teaching with the Sixth Edition.

 


New To This Edition

• New graphics and new text inserted where needed for improved student accessibility and understanding of difficult concepts.

 

• Chapter by chapter changes:

– Chapter 1:

New Figures 1.3.9 and 1.3.10 showing direction fields that illustrate failure of existence and uniqueness of solutions New Problems 34 and 35 showing that small changes in initial conditions can make big differences in results, but big changes in initial conditions may sometimes make only small differences in results; new Remarks 1 and 2 clarifying the concept of implicit solutions; new Remark clarifying the meaning of homogeneity for first-order equations; additional details inserted in the derivation of the rocket propulsion equationand new Problem 5 inserted to investigate the liftoff pause of a rocket on the launch pad sometimes observed before blastoff.

 

– Chapter 2:

New explanation of signs and directions of internal forces in mass-spring systems; new introduction of differential operators and clarification of the algebra of polynomial operators; new introduction and illustration of polar exponential forms of complex numbers; fuller explanation of method of undetermined coefficients in Examples 1 and 3; new Remarks 1 and 2 introducing "shooting" terminology, and new Figures 2.8.1 and 2.8.2 illustrating why some endpoint value problems have infinitely many solutions, while others have no solutions at all; new Figures 2.8.4 and 2.8.5 illustrating different types of eigenfunctions.

 

– Chapter 3: New Problem 35 on determination of radii of convergence of power series solutions of differential equations; new Example 3 just before the subsection on logarithmic cases in the method of Frobenius, to illustrate first the reduction-of-order formula with a simple non-series problem.

 

– Chapter 4: New discussion clarifying functions of exponential order and existence of Laplace transforms; new Remark discussing the mechanics of partial-fraction decomposition; new much-expanded discussion of the proof of the Laplace-transform existence theorem and its extension to include the jump discontinuities that play an important role in many practical applications.

 

– Chapter 5: New Problems 20—23 for student exploration of three-railway-cars systems with different initial velocity conditions; new Remark illustrating the relation between matrix exponential methods and the generalized eigenvalue methods discussed previously; new exposition inserted at end of section to explain the connection between matrix variation of parameters here and (scalar) variation of parameters for second-order equations discussed previously in Chapter 3.

 

– Chapter 6: New discussion with new Figures 6.3.11 and 6.3.12 clarifying the difference between rotating and non-rotating coordinate systems in moon-earth orbit problems.

 

– Chapter 7: New remarks on phase plane portraits, autonomous systems, and critical points; new introduction of linearized systems; new 3-dimensional Figures 6.5.18 and 6.5.20 illustrating Lorenz and Rössler trajectories.

 

 

 

 


Table of Contents

C O N T E N T S

Preface vii

CHAPTER

1 First-Order Differential Equations 1

1.1 Differential Equations and Mathematical Models 1

1.2 Integrals as General and Particular Solutions 10

1.3 Slope Fields and Solution Curves 19

1.4 Separable Equations and Applications 32

1.5 Linear First-Order Equations 46

1.6 Substitution Methods and Exact Equations 59

1.7 Population Models 74

1.8 Acceleration-Velocity Models 85

CHAPTER

2 Linear Equations of Higher Order 100

2.1 Introduction: Second-Order Linear Equations 100

2.2 General Solutions of Linear Equations 113

2.3 Homogeneous Equations with Constant Coefficients 124

2.4 Mechanical Vibrations 135

2.5 Nonhomogeneous Equations and Undetermined Coefficients 148

2.6 Forced Oscillations and Resonance 162

2.7 Electrical Circuits 173

2.8 Endpoint Problems and Eigenvalues 180

CHAPTER

3 Power Series Methods 194

3.1 Introduction and Review of Power Series 194

3.2 Series Solutions Near Ordinary Points 207

3.3 Regular Singular Points 218

3.4 Method of Frobenius: The Exceptional Cases 233

3.5 Bessel's Equation 248

3.6 Applications of Bessel Functions 257

v

vi Contents

CHAPTER

4 Laplace Transform Methods 266

4.1 Laplace Transforms and Inverse Transforms 266

4.2 Transformation of Initial Value Problems 277

4.3 Translation and Partial Fractions 289

4.4 Derivatives, Integrals, and Products of Transforms 297

4.5 Periodic and Piecewise Continuous Input Functions 304

4.6 Impulses and Delta Functions 316

CHAPTER

5 Linear Systems of Differential Equations 326

5.1 First-Order Systems and Applications 326

5.2 The Method of Elimination 338

5.3 Matrices and Linear Systems 347

5.4 The Eigenvalue Method for Homogeneous Systems 366

5.5 Second-Order Systems and Mechanical Applications 381

5.6 Multiple Eigenvalue Solutions 393

5.7 Matrix Exponentials and Linear Systems 407

5.8 Nonhomogeneous Linear Systems 420

CHAPTER

6 Numerical Methods 430

6.1 Numerical Approximation: Euler's Method 430

6.2 A Closer Look at the Euler Method 442

6.3 The Runge-Kutta Method 453

6.4 Numerical Methods for Systems 464

CHAPTER

7 Nonlinear Systems and Phenomena 480

7.1 Equilibrium Solutions and Stability 480

7.2 Stability and the Phase Plane 488

7.3 Linear and Almost Linear Systems 500

7.4 Ecological Models: Predators and Competitors 513

7.5 Nonlinear Mechanical Systems 526

7.6 Chaos in Dynamical Systems 542

References for Further Study 555

Appendix: Existence and Uniqueness of Solutions 559

Answers to Selected Problems 573

Index I-1

 



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Instructor's Solutions Manual (Download only) for Elementary Differential Equations, 6/E
Edwards
©2008  |  Pearson  |  On-line Supplement  |  Live
ISBN-10: 0136006140  |  ISBN-13: 9780136006145

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Student resources

Applications Manual for Differential Equations and Boundary Value Problems: Computing and Modeling, 4/E
Edwards & Penney
©2008  |  Pearson  |  Paper; 352 pp  |  Instock
ISBN-10: 0136006795  |  ISBN-13: 9780136006794
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Student Solutions Manual for Elementary Differential Equations, 6/E
Edwards
©2008  |  Pearson  |  Paper; 352 pp  |  Instock
ISBN-10: 0136006159  |  ISBN-13: 9780136006152
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Ordinary Differential Equations Using MATLAB, 3/E
Polking
©2004  |  Pearson  |  Paper; 264 pp  |  Instock
ISBN-10: 0131456792  |  ISBN-13: 9780131456792
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