An Elementary Course in Partial Differential Equations - Hardcover

Amaranath, T.

Hardcover

ISBN 10: 1842651560 ISBN 13: 9781842651568

Publisher: Alpha Science, 2003

Synopsis

The long awaited second edition of this very successful textbook for graduate students covers the study of first and second order of Partial Differential Equations. With a simplified but highly effective method of presentation, this edition offers a greater number of exercises and worked examples as the end of each section, making this an ideal book for those preparing for the CSIR/UGC, GATE and UPSC examinations.

Table of Contents

• Preface
•

• Preface to the Second Edition
• First Order P.D.E.
• Curves and Surfaces
• Genesis of First Order P.D.E.
• Classification of Integrals
• Linear Equations of the First Order Pfaffian Differential Equations
• Compatible Systems
• Charpit's Method
• Jacobi's Method
• Integral Surface Through a Given Curve
• Quasi-Linear Equations
• Non-Linear First Order P.D.E.
• Second Order P.D.E
• Genesis of Second Order P.D.E.
• Classification of Second Order P.D.E.
• One Dimensional Wave Equation
• Vibrations of an Infinite String
• Vibrations of a Semi-infinite String
• Vibrations of a String of Finite Length
• Riemann's Method
• Vibrations of a String of Finite Length (Method of Separation of Variables)
• Laplace's Equation
• Boundary Value Problems
• Maximum and Minimum Principles
• The Cauchy Problem
• The Dirichlet Problem for the Upper Half Plane
• The Neumann Problem for the Upper Half Plane
• The Dirichlet Problem for a Circle
• The Dirichlet Exterior Problem for a Circle
• The Neumann Problem for a Circle
• The Dirichlet Problem for a Rectangle
• Harnack's Theorem
• Laplace's Equation Green's Function
• The Dirichlet Problem for a Half Plane
• The Dirichlet Problem for a Circle
• Heat Conduction Problem
• Heat Conduction Infinite Rod Case
• Heat Conduction Finite Rod Case
• Duhamel's Principle
• Wave Equation
• Heat Conduction Equation
• Classification in the Case of n-Variables
• Families of Equipotential Surfaces
• Kelvin's Inversion Theorem
• A Fourier Transforms and Integrals
• Fourier Integral Theorem
• Properties of Fourier Transform
• Examples
• Convolution Theorem
• Vibrations of an Infinite String
• Suggested Readings
• Index

About this title

About the Author

T. Amaranath.: Department of Mathematics and Statistics, University of Hyderabad, Hyderabad, India

Edition details

• Publisher: Alpha Science
• Publication date: 2003
• Language: English
• ISBN 10: 1842651560
• ISBN 13: 9781842651568
• Binding: Hardcover
• Edition number: 2
• Number of pages: 164