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Product Code:  AMSIP/6 
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Electronic ISBN:  9781470437978 
Product Code:  AMSIP/6.E 
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Book DetailsAMS/IP Studies in Advanced MathematicsVolume: 6; 1997; 706 ppMSC: Primary 35;
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
ReadershipGraduate students and research mathematicians interested in partial differential equations.

Table of Contents

Chapters

Introduction

Partial differentiation

Solutions of PDE’s and their specification

PDE’s and related arbitrary functions

Particular solutions of PDE’s

Similarity solutions

Correctly set problems

Some preliminary aspects of linear first order PDE’s

Linear first order PDE’s with two independent variables

First order nonlinear PDE’s

Some technical problems and related PDE’s

Linear first order PDE’s with two independent variables, general theory

First order PDE’s with multiple independent variables

Original details of the Fourier approach to boundary value problems

Eigenfunctions and eigenvalues

Eigenfunctions and eigenvalues, continued

Nonorthogonal eigenfunctions

Further example of Fourier style analysis

Inhomogeneous problems

Local heat sources

An inhomogeneous configuration

Other eigenfunction/eigenvalue problems

Uniqueness of solutions

Alternative representations of solutions

Other differential equations and inferences therefrom

Second order ODE’s

Boundary value problems and SturmLiouville theory

Green’s functions and boundary value problems

Green’s functions and generalizations

PDE’s, Green’s functions, and integral equations

Singular and infinite range problems

Orthogonality and its ramifications

Fourier expansions: Generalities

Fourier expansions: Varied examples

Fourier integrals and transforms

Applications of Fourier transforms

Legendre polynomials and related expansions

Bessel functions and related expansions

Hyperbolic equations


Reviews

A large variety of examples and problems for solutions is given … The book will be certainly of great value with respect to applications.
Monatshefte für Mathematik 
Although the scope is large—there are 706 pages—the chapters tend to be short and to the point, with the detailed work developed in the problems set at the end of each chapter. These problem sets should ideally provide instructors delivering an advanced mathematical methods course with plenty of ideas for tutorial material for their students. The book is comprehensive in its background coverage, including, for example, an introductory chapter on partial differentiation, which at the same time brings in and manipulates a couple of wellknown canonical forms, by way of illustration. In all, this text is a useful addition to the extensive literature on PDEs.
Mathematical Reviews 
Naturally the book will be helpful for a very wide audience which would benefit from reading it–from students and Ph.D. candidates (not only of mathematical direction) to specialists. This book can be recommended as a well written handbook containing an original approach to the description of basic and advanced methods of the theory of PDE.
Zentralblatt MATH


Request Review Copy
 Book Details
 Table of Contents
 Reviews

 Request Review Copy
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Graduate students and research mathematicians interested in partial differential equations.

Chapters

Introduction

Partial differentiation

Solutions of PDE’s and their specification

PDE’s and related arbitrary functions

Particular solutions of PDE’s

Similarity solutions

Correctly set problems

Some preliminary aspects of linear first order PDE’s

Linear first order PDE’s with two independent variables

First order nonlinear PDE’s

Some technical problems and related PDE’s

Linear first order PDE’s with two independent variables, general theory

First order PDE’s with multiple independent variables

Original details of the Fourier approach to boundary value problems

Eigenfunctions and eigenvalues

Eigenfunctions and eigenvalues, continued

Nonorthogonal eigenfunctions

Further example of Fourier style analysis

Inhomogeneous problems

Local heat sources

An inhomogeneous configuration

Other eigenfunction/eigenvalue problems

Uniqueness of solutions

Alternative representations of solutions

Other differential equations and inferences therefrom

Second order ODE’s

Boundary value problems and SturmLiouville theory

Green’s functions and boundary value problems

Green’s functions and generalizations

PDE’s, Green’s functions, and integral equations

Singular and infinite range problems

Orthogonality and its ramifications

Fourier expansions: Generalities

Fourier expansions: Varied examples

Fourier integrals and transforms

Applications of Fourier transforms

Legendre polynomials and related expansions

Bessel functions and related expansions

Hyperbolic equations

A large variety of examples and problems for solutions is given … The book will be certainly of great value with respect to applications.
Monatshefte für Mathematik 
Although the scope is large—there are 706 pages—the chapters tend to be short and to the point, with the detailed work developed in the problems set at the end of each chapter. These problem sets should ideally provide instructors delivering an advanced mathematical methods course with plenty of ideas for tutorial material for their students. The book is comprehensive in its background coverage, including, for example, an introductory chapter on partial differentiation, which at the same time brings in and manipulates a couple of wellknown canonical forms, by way of illustration. In all, this text is a useful addition to the extensive literature on PDEs.
Mathematical Reviews 
Naturally the book will be helpful for a very wide audience which would benefit from reading it–from students and Ph.D. candidates (not only of mathematical direction) to specialists. This book can be recommended as a well written handbook containing an original approach to the description of basic and advanced methods of the theory of PDE.
Zentralblatt MATH