An Elementary Course in Partial Differential Equations

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

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