Elementary Differential Equations with Boundary Value Problems

ISBN-10: 0136006132
ISBN-13: 9780136006138
Edition: 6th 2008
List price: $213.40 Buy it from $30.12 Rent it from $27.62
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Description: This book enables readers to first solve those differential equations that have the most frequent and interesting applications. This approach illustrates the standard elementary techniques of solution of differential equations. Precise and clear-cut  More...

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Book details

List price: $213.40
Edition: 6th
Copyright year: 2008
Publisher: Prentice Hall PTR
Publication date: 11/30/2007
Binding: Hardcover
Pages: 792
Size: 8.25" wide x 10.75" long x 1.25" tall
Weight: 4.026
Language: English

This book enables readers to first solve those differential equations that have the most frequent and interesting applications. This approach illustrates the standard elementary techniques of solution of differential equations. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques.The first few sections of most chapters introduce the principle ideas of each topic, with remaining sections devoted to extensions and applications. Topics covered include first-order differential equations, linear equations of higher order, power series methods, Laplace transform methods, linear systems of differential equations, numerical methods, nonlinear systems and phenomena, Fourier series methods, and Eigenvalues and boundary value problems.For those 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
LaplaceTransform 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 Stability
Stability and the Phase Plane
Linear and Almost Linear Systems
Ecological Models: Predators and Competitors
Nonlinear Mechanical Systems
Chaos in Dynamical Systems
Fourier Series Methods
Periodic Functions and Trigonometric Series
General Fourier Series and Convergence
Fourier Sine and Cosine Series
Applications of Fourier Series
Heat Conduction and Separation of Variables
Vibrating Strings and the One-Dimensional Wave Equation
Steady-State Temperature and Laplace's Equation
Eigenvalues and Boundary Value Problems
Sturm-Liouville Problems and Eigenfunction Expansions
Applications of Eigenfunction Series
Steady Periodic Solutions and Natural Frequencies
Cylindrical Coordinate Problems
Higher-Dimensional Phenomena
References for Further Study
Existence and Uniqueness of Solutions
Answers to Selected Problems
Index I-1

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