Partial Differential Equations An Introduction

ISBN-10: 0470054565

ISBN-13: 9780470054567

Edition: 2nd 2008

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Description:

Covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them. Uses a broad approach to illustrate the rich diversity of phenomena such as vibrations of solids, fluid flow, molecular structure, photon and electron interactions, radiation of electromagnetic waves encompassed by this subject as well as the role PDEs play in modern mathematics, especially geometry and analysis.
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Book details

List price: $230.95
Edition: 2nd
Copyright year: 2008
Publisher: John Wiley & Sons, Incorporated
Publication date: 12/21/2007
Binding: Hardcover
Pages: 464
Size: 6.25" wide x 9.50" long x 0.75" tall
Weight: 1.738
Language: English

Where PDEs Come From
What is a Partial Differential Equation?
First-Order Linear Equations
Flows, Vibrations, and Diffusions
Initial and Boundary Conditions
Well-Posed Problems
Types of Second-Order Equations
Waves and Diffusions
The Wave Equation
Causality and Energy
The Diffusion Equation
Diffusion on the Whole Line
Comparison of Waves and Diffusions
Reflections and Sources
Diffusion on the Half-Line
Reflections of Waves
Diffusion with a Source
Waves with a Source
Diffusion Revisited
Boundary Problems
Separation of Variables, The Dirichlet Condition
The Neumann Condition
The Robin Condition
Fourier Series
The Coefficients
Even, Odd, Periodic, and Complex Functions
Orthogonality and General Fourier Series
Completeness
Completeness and the Gibbs Phenomenon
Inhomogeneous Boundary Conditions
Harmonic Functions
Laplace's Equation
Rectangles and Cubes
Poisson's Formula
Circles, Wedges, and Annuli
Green's Identities and Green's Functions
Green's First Identity
Green's Second Identity
Green's Functions
Half-Space and Sphere
Computation of Solutions
Opportunities and Dangers
Approximations of Diffusions
Approximations of Waves
Approximations of Laplace's Equation
Finite Element Method
Waves in Space
Energy and Causality
The Wave Equation in Space-Time
Rays, Singularities, and Sources
The Diffusion and Schrodinger Equations
The Hydrogen Atom
Boundaries in the Plane and in Space
Fourier's Method, Revisited
Vibrations of a Drumhead
Solid Vibrations in a Ball
Nodes
Bessel Functions
Legendre Functions
Angular Momentum in Quantum Mechanics
General Eigenvalue Problems
The Eigenvalues Are Minima of the Potential Energy
Computation of Eigenvalues
Completeness
Symmetric Differential Operators
Completeness and Separation of Variables
Asymptotics of the Eigenvalues
Distributions and Transforms
Distributions
Green's Functions, Revisited
Fourier Transforms
Source Functions
Laplace Transform Techniques
PDE Problems from Physics
Electromagnetism
Fluids and Acoustics
Scattering
Continuous Spectrum
Equations of Elementary Particles
Nonlinear PDEs
Shock Waves
Solitons
Calculus of Variations
Bifurcation Theory
Water Waves
Appendix
Continuous and Differentiable Functions
Infinite Series of Functions
Differentiation and Integration
Differential Equations
The Gamma Function
References
Answers and Hints to Selected Exercises
Index
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