(0) items

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.
Elementary Differential Equations,9780470458327
This item qualifies for

Your order must be $59 or more, you must select US Postal Service Shipping as your shipping preference, and the "Group my items into as few shipments as possible" option when you place your order.

Bulk sales, PO's, Marketplace Items, eBooks, Apparel, and DVDs not included.

Elementary Differential Equations

by ;


Pub. Date:
John Wiley & Sons Inc
List Price: $253.33

Rent Textbook


Buy New Textbook

Usually Ships in 3-4 Business Days



Used Textbook

We're Sorry
Sold Out

More New and Used
from Private Sellers
Starting at $167.19

Questions About This Book?

Why should I rent this book?
Renting is easy, fast, and cheap! Renting from can save you hundreds of dollars compared to the cost of new or used books each semester. At the end of the semester, simply ship the book back to us with a free UPS shipping label! No need to worry about selling it back.
How do rental returns work?
Returning books is as easy as possible. As your rental due date approaches, we will email you several courtesy reminders. When you are ready to return, you can print a free UPS shipping label from our website at any time. Then, just return the book to your UPS driver or any staffed UPS location. You can even use the same box we shipped it in!
What version or edition is this?
This is the 10th edition with a publication date of 10/2/2012.
What is included with this book?
  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.
  • The Rental copy of this book is not guaranteed to include any supplemental materials. You may receive a brand new copy, but typically, only the book itself.
  • The eBook copy of this book is not guaranteed to include any supplemental materials. Typically only the book itself is included.


Boyce/DiPrima is the best-seller in its market and extremely popular. The format remains unchanged, but exercises and examples have been updated to reflect the most current scenarios and topics.

Author Biography

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.

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

Please wait while the item is added to your cart...