Differential Equations and Boundary Value Problems Computing and Modeling

ISBN-10: 0131561073
ISBN-13: 9780131561076
Edition: 4th 2008
List price: $205.00 Buy it from $14.98
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Description: This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments likeMaple, Mathematica,and MATLAB; it does not concentrate on traditional manual  More...

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Book details

List price: $205.00
Edition: 4th
Copyright year: 2008
Publisher: Prentice Hall PTR
Publication date: 7/26/2007
Binding: Hardcover
Pages: 816
Size: 8.00" wide x 10.25" long x 1.25" tall
Weight: 3.696
Language: English

This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments likeMaple, Mathematica,and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications.The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book.For mathematicians and those in the field of computer science and engineering. nbsp;

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
Mathematical Models and Numerical Methods
Population Models
Equilibrium Solutions and Stability
Acceleration-Velocity Models
Numerical Approximation: Euler's Method
A Closer Look at the Euler Method, and Improvements
The Runge-Kutta Method
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
Introduction to Systems of Differential Equations
First-Order Systems and Applications
The Method of Elimination
Numerical Methods for Systems
Linear Systems of Differential Equations
Linear Systems and Matrices
The Eigenvalue Method for Homogeneous Systems
Second Order Systems and Mechanical Applications
Multiple Eigenvalue Solutions
Matrix Exponentials and Linear Systems
Nonhomogenous Linear Systems
Nonlinear Systems and Phenomena
Stability and the Phase Plane
Linear and Almost Linear Systems
Ecological Models: Predators and Competitors
Nonlinear Mechanical Systems
Chaos in Dynamical Systems
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 Forcing Functions
Impulses and Delta Functions
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
Fourier Series Methods
Periodic Functions and Trigonometric Series
General Fourier Series and Convergence
Even-Odd Functions and Termwise Differentiation
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
Applications of Bessel Functions
Higher-Dimensional Phenomena
References
Appendix: Existence and Uniqueness of Solutions
Answers to Selected Problems
Index

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