Elementary Differential Equations / Edition 10

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Overview

Retaining the same general organizational structure as its popular predecessors, this edition combines a sound and accurate exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation which have proved useful in a wide variety of applications. This updated text includes nearly 300 new problems, many of which assume the availability of computers; an expanded discussion of error control and stability; numerous new and revised problems and examples that investigate the manner in which a solution depends on one or more parameters; and greater emphasis on visualization.
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Editorial Reviews

Booknews
To accommodate the changing learning environment, this edition takes a more visual, quantitative, project, and example-oriented approach for undergraduate students in mathematics, science, or engineering whose interest in differential equations ranges from the totally theoretical to the diehard practical. Other changes include an introduction to mathematical modeling, direction fields, the basic ideas of stability and instability, and Euler's method of numerical approximation. Coverage includes first-, second-, and higher-order linear and nonlinear equations; the Laplace transform; and numerical methods. Includes chapter problems and appended answers. Boyce is professor emeritus, and DiPrima is a professor, respectively, in the department of mathematical sciences at Rensselaer Polytechnic Institute in Troy, New York. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780470458327
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 10/2/2012
  • Edition description: New Edition
  • Edition number: 10
  • Pages: 672
  • Sales rank: 163,729
  • Product dimensions: 8.40 (w) x 10.10 (h) x 1.10 (d)

Meet the Author

Dr. Boyce received his B.A. degree in Mathematics from Rhodes College, and his M.S. and Ph.D. degrees in Mathematics from Carnegie-Mellon University. He is a member of the American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. He is currently the Edward P. Hamilton Distinguished Professor Emeritus of Science Education (Department of Mathematical Sciences) at Rensselaer. He is the author of numerous technical papers in boundary value problems and random differential equations and their applications. He is the author of several textbooks including two differential equations texts. In 1991 he received the William H.Wiley Distinguished Faculty Award given by Rensselaer.

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Table of Contents

Chapter 1 Introduction 1

1.1 Some Basic Mathematical Models; Direction Fields 1

1.2 Solutions of Some Differential Equations 10

1.3 Classification of Differential Equations 19

1.4 Historical Remarks 26

Chapter 2 First Order Differential Equations 31

2.1 Linear Equations; Method of Integrating Factors 31

2.2 Separable Equations 42

2.3 Modeling with First Order Equations 51

2.4 Differences Between Linear and Nonlinear Equations 68

2.5 Autonomous Equations and Population Dynamics 78

2.6 Exact Equations and Integrating Factors 95

2.7 Numerical Approximations: Euler’s Method 102

2.8 The Existence and Uniqueness Theorem 112

2.9 First Order Difference Equations 122

Chapter 3 Second Order Linear Equations 137

3.1 Homogeneous Equations with Constant Coefficients 137

3.2 Solutions of Linear Homogeneous Equations; the Wronskian 145

3.3 Complex Roots of the Characteristic Equation 158

3.4 Repeated Roots; Reduction of Order 167

3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 175

3.6 Variation of Parameters 186

3.7 Mechanical and Electrical Vibrations 192

3.8 Forced Vibrations 207

Chapter 4 Higher Order Linear Equations 221

4.1 General Theory of nth Order Linear Equations 221

4.2 Homogeneous Equations with Constant Coefficients 228

4.3 The Method of Undetermined Coefficients 236

4.4 The Method of Variation of Parameters 241

Chapter 5 Series Solutions of Second Order Linear Equations 247

5.1 Review of Power Series 247

5.2 Series Solutions Near an Ordinary Point, Part I 254

5.3 Series Solutions Near an Ordinary Point, Part II 265

5.4 Euler Equations; Regular Singular Points 272

5.5 Series Solutions Near a Regular Singular Point, Part I 282

5.6 Series Solutions Near a Regular Singular Point, Part II 288

5.7 Bessel’s Equation 296

Chapter 6 The Laplace Transform 309

6.1 Definition of the Laplace Transform 309

6.2 Solution of Initial Value Problems 317

6.3 Step Functions 327

6.4 Differential Equations with Discontinuous Forcing Functions 336

6.5 Impulse Functions 343

6.6 The Convolution Integral 350

Chapter 7 Systems of First Order Linear Equations 359

7.1 Introduction 359

7.2 Review of Matrices 368

7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors 378

7.4 Basic Theory of Systems of First Order Linear Equations 390

7.5 Homogeneous Linear Systems with Constant Coefficients 396

7.6 Complex Eigenvalues 408

7.7 Fundamental Matrices 421

7.8 Repeated Eigenvalues 429

7.9 Nonhomogeneous Linear Systems 440

Chapter 8 Numerical Methods 451

8.1 The Euler or Tangent Line Method 451

8.2 Improvements on the Euler Method 462

8.3 The Runge–Kutta Method 468

8.4 Multistep Methods 472

8.5 Systems of First Order Equations 478

8.6 More on Errors; Stability 482

Chapter 9 Nonlinear Differential Equations and Stability 495

9.1 The Phase Plane: Linear Systems 495

9.2 Autonomous Systems and Stability 508

9.3 Locally Linear Systems 519

9.4 Competing Species 531

9.5 Predator–Prey Equations 544

9.6 Liapunov’s Second Method 554

9.7 Periodic Solutions and Limit Cycles 565

9.8 Chaos and Strange Attractors: The Lorenz Equations 577

Answers to Problems 589

Index 637

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Customer Reviews

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  • Anonymous

    Posted April 28, 2001

    Good exercises, but a little wordy for an intro course

    I used this course in an introductory differential equations course targeted at engineers, physicists, chemists, and mathematicians. Coupled with a good instructor, it can be a valuable tool. My favorite feature is the inclusion of solutions (in the back of the book) to ALL exercises that do not require plotting. This helped me to learn much more as I always worked out my solutions until I had the right answer, knowing that the process is the most important. It is a little long to read everything in a section, so it needs to be used by a good instructor, but not too bad overall.

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