Elementary Differential Equations / Edition 9

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Overview

Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies.
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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: 9780470039403
  • Publisher: Wiley
  • Publication date: 10/13/2008
  • Edition description: Older Edition
  • Edition number: 9
  • Pages: 656
  • Product dimensions: 8.30 (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

Preface 
Chapter 1 Introduction 1
1.1  Some Basic Mathematical Models; Direction Fields 
1.2  Solutions of Some Differential Equations 
1.3  Classification of Differential Equations 
1.4  Historical Remarks

Chapter 2 First Order Differential Equations 
2.1  Linear Equations; Method of Integrating Factors 
2.2 Separable Equations 
2.3 Modeling with First Order Equations 
2.4 Differences Between Linear and Nonlinear Equations
2.5 Autonomous Equations and Population Dynamics
2.6 Exact Equations and Integrating Factors 
2.7 Numerical Approximations: Euler's Method 
2.8 The Existence and Uniqueness Theorem
2.9 First Order Difference Equations 

Chapter 3 SecondOrder Linear Equations 135
3.1 Homogeneous Equations with Constant Coef?cients 
3.2 Fundamental Solutions of Linear Homogeneous Equations; The Wronskian 
3.3 Complex Roots of the Characteristic Equation 
3.4 Repeated Roots; Reduction of Order
3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients 
3.6 Variation of Parameters
3.7 Mechanical and Electrical Vibrations
3.8 Forced Vibrations

Chapter 4 Higher Order Linear Equations 
4.1 General Theory of nth Order Linear Equations
4.2 Homogeneous Equations with Constant Coef?cients 
4.3 The Method of Undetermined Coef?cients 
4.4 The Method of Variation of Parameters

Chapter 5 Series Solutions of Second Order Linear Equations 
5.1 Review of Power Series 
5.2 Series Solutions Near an Ordinary Point, Part I 
5.3 Series Solutions Near an Ordinary Point, Part II 
5.4 Euler Equations; Regular Singular Points 
5.5 Series Solutions Near a Regular Singular Point, Part I 
5.6 Series Solutions Near a Regular Singular Point, Part II 
5.7  Bessel's Equation 

Chapter 6 The Laplace Transform
6.1 Definition of the Laplace Transform 
6.2 Solution of Initial Value Problems 
6.3 Step Functions 
6.4 Differential Equations with Discontinuous Forcing Functions 
6.5 Impulse Functions 
6.6 The Convolution Integral 

Chapter 7 Systems of First Order Linear Equations 
7.1 Introduction 
7.2 Review of Matrices 
7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors 
7.4 Basic Theory of Systems of First Order Linear Equations
7.5 Homogeneous Linear Systems with Constant Coefficients 
7.6 Complex Eigenvalues 
7.7 Fundamental Matrices 
7.8 Repeated Eigenvalues 
7.9 Nonhomogeneous Linear Systems 

Chapter 8 Numerical Methods
8.1 The Euler or Tangent Line Method
8.2 Improvements on the Euler Method 
8.3 The Runge-KuttaMethod
8.4 Multistep Methods 
8.5 More on Errors; Stability 
8.6 Systems of First Order Equations

Chapter 9 Nonlinear Differential Equations and Stability
9.1 The Phase Plane: Linear Systems 
9.2 Autonomous Systems and Stability 
9.3 Locally Linear Systems
9.4 Competing Species
9.5 Predator-Prey Equations 
9.6 Liapunov's Second Method 
9.7 Periodic Solutions and Limit Cycles 
9.8 Chaos and Strange Attractors: The Lorenz Equations 
Answers to Problems 
Index 

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