Textbook

# Elementary Differential Equations and Boundary Value Problems, 10th Edition

## Description

The 10th edition of Elementary Differential Equations and Boundary Value Problems, like its predecessors, is written  from the viewpoint of the applied mathematician, whose interest in  differential equations may sometimes be quite theoretical,  sometimes intensely practical, and often somewhere in between. The authors have sought to combine a sound and accurate exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 10th edition includes new problems, updated figures and examples to help motivate students.  The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study.

WileyPLUS sold separately from text.

See More

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

Chapter 10 Partial Differential Equations and Fourier Series 589

10.1 Two-Point Boundary Value Problems 589

10.2 Fourier Series 596

10.3 The Fourier Convergence Theorem 607

10.4 Even and Odd Functions 614

10.5 Separation of Variables; Heat Conduction in a Rod 623

10.6 Other Heat Conduction Problems 632

10.7 TheWave Equation: Vibrations of an Elastic String 643

10.8 Laplace’s Equation 658

AppendixA Derivation of the Heat Conduction Equation 669

Appendix B Derivation of theWave Equation 673

Chapter 11 Boundary Value Problems and Sturm–Liouville Theory 677

11.1 The Occurrence of Two-Point Boundary Value Problems 677

11.2 Sturm–Liouville Boundary Value Problems 685

11.3 Nonhomogeneous Boundary Value Problems 699

11.4 Singular Sturm–Liouville Problems 714

11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion 721

11.6 Series of Orthogonal Functions: Mean Convergence 728

Index 799

See More

## New To This Edition

• Sections 8.5 and 8.6 have been interchanged, so that the more advanced topics appear at the end of the chapter.
• Derivations and proofs in several chapters have been expanded or rewritten to provide more details.
• The fact that the real and imaginary parts of a complex solution of a real problem are also solutions now appears as a theorem in Sections 3.2 and 7.4.
• The treatment of generalized eigenvectors in Section 7.8 has been expanded both in the text and in the problems.
• There are about twenty new or revised problems scattered throughout the book.
• There are new examples in Sections 2.1, 3.8, and 7.5.
• About a dozen figures have been modified, mainly by using color to make the essential feature of the figure more prominent. In addition, numerous captions have been expanded to clarify the purpose of the figure without requiring a search of the surrounding text.
• There are several new historical footnotes and some others have been expanded.

See More

• A flexible approach to content. Self?]contained chapters allow instructors to customize the selection, order, and depth of chapters.
• A flexible approach to technology. Boyce/DiPrima is adaptable to courses having various levels of computer involvement, ranging from little or none to intensive. More than 450 problems are marked with a technology icon to indicate those that are considered to be technology intensive.
• Sound and accurate exposition of theory. Special attention is made to methods of solution, analysis, and approximation.
• Outstanding exercise sets. Boyce/DiPrima remains unrivaled in quantity, variety, and range providing great flexibility in homework assignments.
• Applied Problems. Many problems ask the student not only to solve a differential equation but also to draw conclusions from the solution, reflecting the usual situation in scientific or engineering applications.
• Historical footnotes. The footnotes allow the student to trace the development of the discipline and identify outstanding individual contributions.

See More
Instructors Resources
Wiley Instructor Companion Site
Instructor’s Solutions Manual
PowerPoint slides
Chapter Review Sheets
Brannan/Boyce Projects
Interactive Demonstrations Applets
Maple™ Technology Resources
Mathematica™ Technology Resources
Matlab™ Technology Resources
Image Gallery
Art PowerPoint slides
A research-based online environment for learning and assessment.
Request a print evaluation copy
See More
See Less
Students Resources
Wiley Student Companion Site
Chapter Review Sheets
Brannan/Boyce Projects
Interactive Demonstrations Applets
Maple™ Technology Resources
Mathematica™ Technology Resources
Matlab™ Technology Resources
Available Materials
by William E. Boyce, Richard C. DiPrima, Charles W. Haines, Tamas Wiandt
978-0-470-45833-4
A research-based online environment for learning and assessment.
See More
See Less
Purchase Options
Wiley E-Text
Elementary Differential Equations and Boundary Value Problems, 10th Edition
ISBN : 978-1-118-54394-8
832 pages
\$80.00

Loose-leaf
Elementary Differential Equations and Boundary Value Problems, Binder Ready Version, 10th Edition
ISBN : 978-1-118-15738-1
832 pages