Partial Differential Equations and Boundary Value Problems

ISBN-10: 0139586202
ISBN-13: 9780139586200
Edition: 2000
Authors: Nakhle H. Asmar
List price: $100.00
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Description: For introductory courses in PDEs taken by majors in engineering, physics, and mathematics. Packed with examples, this text provides a smooth transition from a course in elementary ordinary differential equations to more advanced concepts in a first  More...

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Book details

List price: $100.00
Copyright year: 2000
Publisher: Prentice Hall PTR
Publication date: 8/17/1999
Binding: Hardcover
Pages: 598
Size: 8.25" wide x 9.50" long x 1.00" tall
Weight: 2.596
Language: English

For introductory courses in PDEs taken by majors in engineering, physics, and mathematics. Packed with examples, this text provides a smooth transition from a course in elementary ordinary differential equations to more advanced concepts in a first course in partial differential equations. Asmar's relaxed style and emphasis on applications make the material understandable even for students with limited exposure to topics beyond calculus. This computer-friendly text encourages the use of computer resources for illustrating results and applications, but it is also suitable for use without computer access. Additional specialized topics are included that are covered independently of each other and can be covered by instructors as desired.

Preface
A Preview of Applications and Techniques
What Is a Partial Differential Equation?
Solving and Interpreting a Partial Differential Equation
Fourier Series
Periodic Functions
Fourier Series
Fourier Series of Functions with Arbitrary Periods
Half-Range Expansions: The Cosine, and Sine Series
Mean Square Approximation and Parseval's Identity
Complex Form of Fourier Series
Supplement on Convergence
Uniform Convergence of Sequences and Series of Functions
Dirichlet Test and Convergence of Fourier Series
Partial Differential Equations in Rectangular Coordinates
Partial Differential Equations in Physics and Engineering
Modeling: Vibrating Strings and the Wave Equation
Solution of the One Dimensional Wave Equation: The Method of Separation of Variables
D'Alembert's Method
The One Dimensional Heat Equation
Heat Conduction in Bars: Varying the Boundary Conditions
The Two Dimensional Wave and Heat Equations
Laplace's Equation in Rectangular Coordinates
Poisson's Equation: The Method of Eigenfunction Expansions
The Maximum Principle
Partial Differential Equations in Polar and Cylindrical Coordinates
The Laplacian in Various Coordinate Systems
Vibrations of a Circular Membrane: Symmetric Case
Vibrations of a Circular Membrane: General Case
Steady-State Temperature in a Disk
Steady-State Temperature in a Cylinder
The Helmholtz and Poisson Equations
Supplement on Bessel Functions
Bessel's Equation and Bessel Functions
Bessel Series Expansions
Partial Differential Equations in Spherical Coordinates
Preview of Problems and Methods
Dirichlet Problems with Symmetry
Spherical Harmonics and the General Dirichlet Problem
The Helmholtz Equation with Applications to the Poisson, Heat, and Wave Equations
Supplement on Legendre Functions
Legendre's Differential Equation
Legendre Polynomials and Legendre Series Expansions
Associated Legendre Functions and Series Expansions
Sturm-Liouville Theory with Engineering Applications
Orthogonal Functions
Sturm-Liouville Theory
The Hanging Chain
Fourth Order Sturm-Liouville Theory
Elastic Vibrations and Buckling of Beams
The Fourier Transform and its Applications
The Fourier Integral Representation
The Fourier Transform
The Fourier Transform Method
The Heat Equation and Gauss's Kernel
A Dirichlet Problem and the Poisson Integral Formula
The Fourier Cosine and Sine Transforms
Problems Involving Semi-Infinite Intervals
The Laplace and Hankel Transforms with Applications
The Laplace Transform
Further Properties of the Laplace Transform
The Laplace Transform Method
The Hankel Transform with Applications
Finite Difference Numerical Methods
The Finite Difference Method for the Heat Equation
The Finite Difference Method for the Wave Equation
The Finite Difference Method for Laplace's Equation
Interation Methods for Laplace's Equation
Sampling and Discrete Fourier Analysis with Applications to Partial Differential Equations
The Sampling Theorem
Partial Differential Equations and the Sampling Theorem
The Discrete and Fast Fourier Transforms
The Fourier and Discrete Fourier Transforms
An Introduction to Quantum Mechanics
Schrodinger's Equation
The Hydrogen Atom
Heisenberg's Uncertainty Principle
Supplement on Orthogonal Polynomials
Hermite and Laguerre Polynomials
Appendixes
Ordinary Differential Equations: Review of Concepts and Methods
Linear Ordinary Differential Equations
Linear Ordinary Differential Equations with Constant Coefficients
Methods for Solving Ordinary Differential Equations
The Method of Power Series
The Method of Frobenius
Tables of Transforms
Fourier Transforms
Fourier Cosine Transforms
Fourier Sine Transforms
Laplace Transforms
References
Answers to Selected Exercises
Index

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