Differential Equations with Boundary Value Problems

ISBN-10: 0131862367
ISBN-13: 9780131862364
Edition: 2nd 2006 (Revised)
List price: $213.40 Buy it from $36.80 Rent it from $22.33
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Description: Combining traditional material with a modern systems approach, this handbook provides a thorough introduction to differential equations, tempering its classic "pure math" approach with more practical applied aspects. Features up-to-date coverage of  More...

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Book details

List price: $213.40
Edition: 2nd
Copyright year: 2006
Publisher: Prentice Hall PTR
Publication date: 7/28/2005
Binding: Hardcover
Pages: 768
Size: 8.25" wide x 10.25" long x 1.00" tall
Weight: 3.630
Language: English

Combining traditional material with a modern systems approach, this handbook provides a thorough introduction to differential equations, tempering its classic "pure math" approach with more practical applied aspects. Features up-to-date coverage of key topics such as first order equations, matrix algebra, systems, and phase plane portraits. Illustrates complex concepts through extensive detailed figures. Focuses on interpreting and solving problems through optional technology projects. For anyone interested in learning more about differential equations.

David Arnold is professor emeritus of Asian and global history in the Department of History at the University of Warwick. Among his numerous works are Science, Technology and Medicine in Colonial India; Gandhi; and The Tropics and the Traveling Gaze: India, Landscape, and Science, 1800-1856.

Preface
Introduction to Differential Equations
Differential Equation Models
The Derivative
Integration
First-Order Equations
Differential Equations and Solutions
Solutions to Separable Equations
Models of Motion
Linear Equations
Mixing Problems
Exact Differential Equations
Existence and Uniqueness of Solutions
Dependence of Solutions on Initial Conditions
Autonomous Equations and Stability
The Daredevil Skydiver
Modeling and Applications
Modeling Population Growth
Models and the Real World
Personal Finance
Electrical Circuits
The Spruce Budworm
Social Security, Now or Later
Second-Order Equations
Definitions and Examples
Second-Order Equations and Systems
Linear, Homogeneous Equations with Constant Coefficients
Harmonic Motion
Inhomogeneous Equations; the Method of Undetermined Coefficients
Variation of Parameters
Forced Harmonic Motion
Nonlinear Oscillators
The Laplace Transform
The Definition of the Laplace Transform
Basic Properties of the Laplace Transform
The Inverse Laplace Transform
Using the Laplace Transform to Solve Differential Equations
Discontinuous Forcing Terms
The Delta Function
Convolutions
Summary
Forced Harmonic Oscillators
Numerical Methods
Euler's Method
Runge-Kutta Methods
Numerical Error Comparisons
Practical Use of Solvers
A Cautionary Tale
Numerical Error Comparison
Matrix Algebra
Vectors and Matrices
The Geometry of Systems of Linear Equations
Solving Systems of Equations
Properties of Solution Sets
Subspaces
Determinants
An Introduction to Systems
Definitions and Examples
Geometric Interpretation of Solutions
Qualitative Analysis
Linear Systems
Long-Term Behavior of Solutions
Linear Systems with Constant Coefficients
Overview of the Technique
Planar Systems
Phase Plane Portraits
Higher Dimensional Systems
The Exponential of a Matrix
Qualitative Analysis of Linear Systems
Higher-Order Linear Equations
Inhomogeneous Linear Systems
Phase Plane Portraits
Oscillations of Linear Molecules
Nonlinear Systems
The Linearization of a Nonlinear System
Long-Term Behavior of Solutions
Invariant Sets and the Use of Nullclines
Long-Term Behavior of Solutions to Planar Systems
Conserved Quantities
Nonlinear Mechanics
The Method of Lyapunov
Predator-Prey Systems
Human Immune Response to Infectious Disease
Analysis of Competing Species
Series Solutions to Differential Equations
Review of Power Series
Series Solutions Near Ordinary Points
Legendre's Equation
Types of Singular Points--Euler's Equation
Series Solutions Near Regular Singular Points
Solutions in the Exceptional Cases
Bessel's Equation and Bessel Functions
Fourier Series
Computation of Fourier Series
Convergence of Fourier Series
Fourier Cosine and Sine Series
The Complex Form of a Fourier Series
The Discrete Fourier Transform and the FFT
Partial Differential Equations
Derivation of the Heat Equation
Separation of Variables for the Heat Equation
The Wave Equation
Laplace's Equation
Laplace's Equation on a Disk
Sturm Liouville Problems
Orthogonality and Generalized Fourier Series
Temperature in a Ball--Legendre Polynomials
Time Dependent PDEs in Higher Dimension
Domains with Circular Symmetry--Bessel Functions
Answers to Odd-Numbered Problems
Index

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