Elementary Differential Equations, 9th Edition

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
Introduction 1
Some Basic Mathematical Models; Direction Fields
Solutions of Some Differential Equations
Classification of Differential Equations
Historical Remarks
First Order Differential Equations
Linear Equations; Method of Integrating Factors
Separable Equations
Modeling with First Order Equations
Differences Between Linear and Nonlinear Equations
Autonomous Equations and Population Dynamics
Exact Equations and Integrating Factors
Numerical Approximations: Euler's Method
The Existence and Uniqueness Theorem
First Order Difference Equations
Second Order Linear Equations 135
Homogeneous Equations with Constant Coef?cients
Fundamental Solutions of Linear Homogeneous Equations; The Wronskian
Complex Roots of the Characteristic Equation
Repeated Roots; Reduction of Order
Nonhomogeneous Equations; Method of Undetermined Coefficients
Variation of Parameters
Mechanical and Electrical Vibrations
Forced Vibrations
Higher Order Linear Equations
General Theory of nth Order Linear Equations
Homogeneous Equations with Constant Coef?cients
The Method of Undetermined Coef?cients
The Method of Variation of Parameters
Series Solutions of Second Order Linear Equations
Review of Power Series
Series Solutions Near an Ordinary Point, Part I
Series Solutions Near an Ordinary Point, Part II
Euler Equations; Regular Singular Points
Series Solutions Near a Regular Singular Point, Part I
Series Solutions Near a Regular Singular Point, Part II
Bessel's Equation
The Laplace Transform
Definition of the Laplace Transform
Solution of Initial Value Problems
Step Functions
Differential Equations with Discontinuous Forcing Functions
Impulse Functions
The Convolution Integral
Systems of First Order Linear Equations
Introduction
Review of Matrices
Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
Basic Theory of Systems of First Order Linear Equations
Homogeneous Linear Systems with Constant Coefficients
Complex Eigenvalues
Fundamental Matrices
Repeated Eigenvalues
Nonhomogeneous Linear Systems
Numerical Methods
The Euler or Tangent Line Method
Improvements on the Euler Method
The Runge-KuttaMethod
Multistep Methods
More on Errors; Stability
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Elementary Differential Equations, 9th Edition

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Elementary Differential Equations, 9th Edition

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