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Introduction to Partial Differential Equations

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ISBN-10: 052161323X

ISBN-13: 9780521613231

Edition: 2005

Authors: Jacob Rubinstein, Yehuda Pinchover

List price: $96.99
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A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional wave equation. Two chapters are devoted to the separation of variables, whilst others concentrate on a wide range of topics including elliptic theory, Green's…    
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Book details

List price: $96.99
Copyright year: 2005
Publisher: Cambridge University Press
Publication date: 5/12/2005
Binding: Paperback
Pages: 384
Size: 6.75" wide x 9.75" long x 0.50" tall
Weight: 1.716
Language: English

Differential operators and the superposition principle
Differential equations as mathematical models
Associated conditions
Simple examples
First-order equations
Quasilinear equations
The method of characteristics
Examples of the characteristics method
The existence and uniqueness theorem
The Lagrange method
Conservation laws and shock waves
The eikonal equation
General nonlinear equations
Second-order linear equations in two indenpendent variables
Canonical form of hyperbolic equations
Canonical form of parabolic equations
Canonical form of elliptic equations
The one-dimensional wave equation
Canonical form and general solution
The Cauchy problem and d' Alembert's formula
Domain of dependence and region of influence
The Cauchy problem for the nonhomogeneous wave equation
The method of separation of variables
Heat equation: homogeneous boundary condition
Separation of variables for the wave equation
Separation of variables for nonhomogeneous equations
The energy method and uniqueness
Further applications of the heat equation
Sturm-Liouville problems and eigenfunction expansions
The Sturm-Liouville problem
Inner product spaces and orthonormal systems
The basic properties of Sturm-Liouville eigenfunctions and eigenvalues
Nonhomogeneous equations
Nonhomogeneous boundary conditions
Elliptic equations
Basic properties of elliptic problems
The maximum principle
Applications of the maximum principle
Green's identities
The maximum principle for the heat equation
Separation of variables for elliptic problems
Poisson's formula
Green's functions and integral representations
Green's function for Dirichlet problem in the plane
Neumann's function in the plane
The heat kernel
Equations in high dimensions
First-order equations
Classification of second-order equations
The wave equation in R[superscript 2] and R[superscript 3]
The eigenvalue problem for the Laplace equation
Separation of variables for the heat equation
Separation of variables for the wave equation
Separation of variables for the Laplace equation
Schrodinger equation for the hydrogen atom
Musical instruments
Green's functions in higher dimensions
Heat kernel in higher dimensions
Variational methods
Calculus of variations
Function spaces and weak formulation
Numerical methods
Finite differences
The heat equation: explicit and implicit schemes, stability, consistency and convergence
Laplace equation
The wave equation
Numerical solutions of large linear algebraic systems
The finite elements method
Solutions of odd-numbered problems
Trigonometric formulas
Integration formulas
Elementary ODEs
Differential operators in polar coordinates
Differential operators in spherical coordinates