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

$116.75

30%OFF

or 4 interest-free payments of $29.19 with

Ships in 15 to 25 business days

This book has been designed for 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

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.

You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Science Physics Science in General Maths for Scientists Engineering & Technology Technology in General Engineering in General Booktopia Publisher Services

World Scientific Publishing

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

Ordinary Differential Equations

Basic Methods, Qualitative Theory, And Fun Models

Stochastic Navier-Stokes Equations on Spheres and Spherical Shells

Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

Topics in Mathematical Modeling by Difference Equations

With Mathematica

Sets and Stability Domains

Time-Varying Nonlinear Systems

Multivariable Calculus Set Free Infinitesimals Ride Again

Infinitesimals Ride Again

Differential Equations, Dynamical Systems, and an Introduction to Chaos, 3e

Differential and Difference Equations in Mathematical Biology

Chapman & Hall/CRC Mathematical Biology Series

Trends in Biomathematics: Complexity Dynamics in Biology, Medicine, and Public Health

Selected Works from the BIOMAT Consortium Lectures, Belgrade, Serbia, 2025

Asymptotic Behavior of Scalar Convection-Diffusion Equations

Springer Monographs in Mathematics

Trends in Applied Mathematical Analysis

Springer Optimization and Its Applications

Sampling, Frames, and Harmonic Analysis

A Mathematical Celebration of Akram Aldroubi's 65th Birthday

Equilibrium and Minimax Problems

Existence, Stability and Algorithms

Advanced Topics on Caputo Tempered Fractional Di?erential Equations with Applications

Form Methods for Evolution Equations

Operator Theory: Advances and Applications

Variational Inequalities

Theory and Applications

Tbilisi Analysis and PDE Seminar

Extended Abstracts of the 2024 Seminar Talks

PDEs, Control and Deep Learning

Cetraro, Italy 2024

Computational Differential Equations with AI

Modern Machine Learning Approaches

From Classical Analysis to Analysis on Fractals

A Tribute to Robert Strichartz, Volume 2

Essays in Analytic Number Theory

In Honor of Helmut Maierâs 70th Birthday

Walter Gautschi, Volume 4

Selected Works with Commentaries

Differential Calculus and its Applications

Quasiperiodic Solutions of the Generalized SQG Equation

Annals of Mathematics Studies

This product is categorised by