An Elementary Course in Partial Differential Equations

ISBN: 1842651560

Author: Amaranath, T.

Condition: New

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