Elementary Differential Equations
10th Edition
Published on 2. October 2012
Book
Mixed media product
672 pages
978-0-470-45832-7 (ISBN)
Description
Elementary Differential Equations, 10th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical and sometimes intensely practical. 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.
More details
Edition
10th edition
Language
English
Place of publication
New York
United States
Target group
College/higher education
Dimensions
Height: 257 mm
Width: 201 mm
Thickness: 25 mm
Weight
1270 gr
ISBN-13
978-0-470-45832-7 (9780470458327)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
William E. Boyce
Elementary Differential Equations and Boundary Value Problems
Loose-leaf edition
09/2016
11th Edition
Wiley
€32.20
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Previous edition
William E. Boyce | Richard C. DiPrima
Elementary Differential Equations
Book
11/2008
9th Edition
Wiley
€65.71
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Persons
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.
Content
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
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