Elementary differential equations
Author(s)
Bibliographic Information
Elementary differential equations
John Wiley & Sons, c2009
9th ed
Available at 4 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Description and Table of Contents
Description
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.
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
by "Nielsen BookData"