Elementary Differential Equations
by Boyce, William E.; DiPrima, Richard C.Edition: 10th
Format: Hardcover
Pub. Date: 2012-10-02
Publisher(s): John Wiley & Sons Inc
Other versions by this Author
-
We Buy This Book Back!
List Price: $272.59
Buy Used
In Stock
$189.99
Rent Textbook
Select for Price
New Textbook
We're Sorry
Sold Out
eTextbook
We're Sorry
Not Available
How Marketplace Works:
- This item is offered by an independent seller and not shipped from our warehouse
- Item details like edition and cover design may differ from our description; see seller's comments before ordering.
- Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
- Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
- Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.
Summary
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
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
Digital License
You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.
More details can be found here.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.