Elementary differential equations (9th Ed.)
Auteur : BOYCE William E.
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...
Date de parution : 11-2008
Ouvrage de 656 p.