Boundary Value Problems

By: Chi Y. Lo

Write A Review

Hardcover | 15 May 2000

At a Glance

Hardcover
272 Pages

Dimensions(cm)
23 x 16.1 x 2

Hardcover

RRP $165.99

$149.75

10%OFF

or 4 interest-free payments of $37.44 with

or

Ships in 15 to 25 business days

This text has been designed for use on a one-year graduate course on boundary value problems for students of mathematics, engineering, and the physical sciences. It deals mainly with the three fundamental equations of mathematical physics, namely the heat equation, the wave equation, and Laplace's equation. The goal of the book is to obtain a formal solution to a given problem either by the method of separation of variables or by the method of general solutions, and to verify that the formal solution possesses all the required properties. To provide the mathematical justification for this approach, the theory of Sturm-Liouville problems, the Fourier series, and the Fourier transform are fully developed. The book assumes a knowledge of advanced calculus and elementary differential equations.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Differential Calculus & Equations

Differential Equations : An Elementary Approach - Rosalind Lake

$290.99

One-Dimensional Ergodic Schrodinger Operators

II. Specific Classes

Paperback

RRP $206.00

$195.75

One-Dimensional Ergodic Schrodinger Operators

II. Specific Classes

Hardcover

RRP $312.00

$290.99

Iterative Methods for Linear and Nonlinear Equations

Frontiers in Applied Mathematics

Paperback

RRP $169.00

$162.75

Functional Analysis

Entering Hilbert Space

Paperback

RRP $81.99

$73.99

10%
OFF

$LEC NOTE MATH OLYM : SNR SEC (V1) - XU JIAGU$

LEC NOTE MATH OLYM

SNR SEC (V1)

Paperback

RRP $77.99

$70.75

Lecture Notes On Mathematical Olympiad Courses

For Senior Section - Volume 2

Paperback

RRP $84.99

$76.75

10%
OFF

Differential Modules over Differential Rings : Chapman & Hall/CRC Monographs and Research Notes in Mathematics - Andy R. Magid

$315.99

14%
OFF

Mathematical Modelling Techniques

Paperback

RRP $147.00

$132.75

10%
OFF

Nonlinear Fractional Differential Equations of Variable Order - Amar Benkerrouche

$195.75

Modelling, Analysis, Monitoring, and Control of Distributed Parameter Systems:

The Tubular Reactor Case Study

Paperback

RRP $194.00

$184.75

Free Boundary Problems Via Da Prato-Grisvard Theory

Paperback

RRP $197.00

$187.75

Preface
Linear Partial Differential Equations	p. 1
Linear problems	p. 1
Classification	p. 5
Well-posed problems	p. 9
Method of general solutions	p. 12
Method of separation of variables	p. 14
The Wave Equation	p. 21
The vibrating string	p. 21
The initial value problem	p. 24
The nonhomogeneous wave equation	p. 29
Uniqueness of the initial value problem	p. 31
Initial-boundary value problems	p. 33
Initial-boundary value problems for semi-infinite string	p. 39
Green's Function and Sturm-Liouville Problems	p. 45
Solutions of second order linear equations	p. 45
Boundary value problems and Green's function	p. 50
Sturm-Liouville problems	p. 58
Convergence in the mean	p. 62
Integral operator with continuous, symmetric kernel	p. 66
Completeness of eigenfunctions of Sturm-Liouville problems	p. 75
Nonhomogeneous integral equation	p. 78
Further properties of eigenvalues and eigenfunctions	p. 81
Fourier Series and Fourier Transforms	p. 95
Trigonometric Fourier series	p. 95
Uniform convergence and completeness	p. 99
Other types of Fourier series	p. 102
Application to the wave equation	p. 105
Fourier integrals	p. 109
Fourier transforms	p. 113
Contour integration	p. 117
The Heat Equation	p. 127
Derivation of the heat equation	p. 127
Maximum principle	p. 130
The initial-boundary value problem	p. 133
Nonhomogeneous problems and finite Fourier transform	p. 135
The initial value problem	p. 138
The initial value problem for the nonhomogeneous equation	p. 142
Nonhomogeneous boundary conditions for initial-boundary value problems	p. 145
Laplace's Equation and Poisson's Equation	p. 151
Boundary value problems	p. 151
Green's identities and uniqueness theorems	p. 152
Maximum principle	p. 154
Laplace's equation in a rectangle	p. 155
Laplace's equation in disc	p. 158
Poisson's integral formula	p. 162
Green's function for Laplace's equation	p. 166
Poisson's equation in a disc	p. 173
Finite Fourier transform for Poisson's equation	p. 177
Dirichlet problem in the upper-half plane	p. 181
Problems in Higher Dimensions	p. 191
Classification	p. 191
Double Fourier series	p. 194
Laplace's equation in a cube	p. 200
The two-dimensional wave equation in a rectangular domain	p. 202
Bessel functions	p. 205
Singular Sturm-Liouville problem for Bessel's equation	p. 209
The two-dimensional wave equation in a circular domain	p. 212
Initial-boundary value problems for the heat equation	p. 217
Legendre's equation	p. 221
Properties of Legendre polynomials	p. 224
Legendre series and boundary value problems	p. 229
Laplace's equation in a sphere	p. 232
Poisson's integral formula in space	p. 235
Ascoli's Theorem	p. 243
App. B: Answers for Selected Problems	p. 245
Bibliography	p. 255
Index	p. 256
Table of Contents provided by Blackwell. All Rights Reserved.

Boundary Value Problems

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Differential Calculus & Equations

Differential Equations

An Elementary Approach

Free Boundary Problems and Regularity Theory

The Secret Life of Equations

The 50 Greatest Equations and How They Work

Recent Progress in Special Functions

Contemporary Mathematics

One-Dimensional Ergodic Schrodinger Operators

II. Specific Classes

One-Dimensional Ergodic Schrodinger Operators

II. Specific Classes

Iterative Methods for Linear and Nonlinear Equations

Frontiers in Applied Mathematics

Functional Analysis

Entering Hilbert Space

LEC NOTE MATH OLYM

SNR SEC (V1)

Lecture Notes On Mathematical Olympiad Courses

For Senior Section - Volume 2

Differential Modules over Differential Rings

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Mathematical Modelling Techniques

Mathematical Modelling Techniques

Nonlinear Fractional Differential Equations of Variable Order

A Course on Function Spaces I

Continuous and Integrable Functions

Variational Methods in Nonlinear Analysis

Optimization and Partial Differential Equations Applications

Differential and Difference Equations with Applications in Queueing Theory

Implicit-Explicit Methods for Evolutionary Partial Differential Equations

Modelling, Analysis, Monitoring, and Control of Distributed Parameter Systems:

The Tubular Reactor Case Study

Free Boundary Problems Via Da Prato-Grisvard Theory

Multivariable Calculus Set Free

Infinitesimals Ride Again

The Calderon Problem

An Introduction

The Calderon Problem

An Introduction

Unbounded Operators and Subnormality

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

This product is categorised by