Elementary Differential Equations

ISBN-10: 0132397307
ISBN-13: 9780132397308
Edition: 6th 2008
List price: $162.00 Buy it from $28.00
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Description: This book gives readers the means to solve differential equations that enjoy the most frequent and interesting applications. It illustrates the standard elementary techniques of solving differential equations, and presents precise and clear-cut  More...

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Book details

List price: $162.00
Edition: 6th
Copyright year: 2008
Publisher: Prentice Hall PTR
Publication date: 11/28/2007
Binding: Hardcover
Pages: 648
Size: 8.00" wide x 10.00" long x 1.25" tall
Weight: 2.882

This book gives readers the means to solve differential equations that enjoy the most frequent and interesting applications. It illustrates the standard elementary techniques of solving differential equations, and presents precise and clear-cut statements of the fundamental existence and uniqueness theorems. Appropriate existence and uniqueness proofs are included in the Appendix.Most chapters introduce the principal ideas of the topic in the first few sections, with the remaining sections devoted to extensions and applications. The widespread use of computer programs for the numerical solution of differential equations is reflected; new problems and computer-generated figures enable readers to construct their own solutions.For readers involved in the fields of science, engineering, and mathematics.

Preface
First-Order Differential Equations
Differential Equations and Mathematical Models
Integrals as General and Particular Solutions
Slope Fields and Solution Curves
Separable Equations and Applications
Linear First-Order Equations
Substitution Methods and Exact Equations
Population Models
Acceleration-Velocity Models
Linear Equations of Higher Order
Introduction: Second-Order Linear Equations
General Solutions of Linear Equations
Homogeneous Equations with Constant Coefficients
Mechanical Vibrations
Nonhomogeneous Equations and Undetermined Coefficients
Forced Oscillations and Resonance
Electrical Circuits
Endpoint Problems and Eigenvalues
Power Series Methods
Introduction and Review of Power Series
Series Solutions Near Ordinary Points
Regular Singular Points
Method of Frobenius: The Exceptional Cases
Bessel's Equation
Applications of Bessel Functions
Laplace Transform Methods
Laplace Transforms and Inverse Transforms
Transformation of Initial Value Problems
Translation and Partial Fractions
Derivatives, Integrals, and Products of Transforms
Periodic and Piecewise Continuous Input Functions
Impulses and Delta Functions
Linear Systems of Differential Equations
First-Order Systems and Applications
The Method of Elimination
Matrices and Linear Systems
The Eigenvalue Method for Homogeneous Systems
Second-Order Systems and Mechanical Applications
Multiple Eigenvalue Solutions
Matrix Exponentials and Linear Systems
Nonhomogeneous Linear Systems
Numerical Methods
Numerical Approximation: Euler's Method
A Closer Look at the Euler Method
The Runge-Kutta Method
Numerical Methods for Systems
Nonlinear Systems and Phenomena
Equilibrium Solutions and Sta

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