Elementary differential equations (9^th Ed.)

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.

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
2.2Separable 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
5.1Review of Power Series
5.2Series Solutions Near an Ordinary Point, Part I
5.3Series Solutions Near an Ordinary Point, Part II
5.4Euler Equations, Regular Singular Points
5.5Series Solutions Near a Regular Singular Point, Part I
5.6Series Solutions Near a Regular Singular Point, Part II
5.7 Bessel"s Equation

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

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

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

Chapter 9 Nonlinear Differential Equations and Stability
9.1The Phase Plane: Linear Systems
9.2Autonomous Systems and Stability
9.3Locally Linear Systems
9.4Competing Species
9.5Predator-Prey Equations
9.6Liapunov"s Second Method
9.7Periodic Solutions and Limit...

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