Partial Differential Equations: An Introductory Treatment With Applications

This book presents comprehensive coverage of the fundamental concepts and applications of partial differential equations (PDEs). It is designed for the undergraduate [BA/BSc (Hons.)] and postgraduate (MA/MSc) students of mathematics, and conforms to the course curriculum prescribed by UGC. The text is broadly organized into two parts. The first part (Lessons 1 to 15) mostly covers the first-order equations in two variables. In these lessons, the mathematical importance of PDEs of first order in physics and applied sciences has also been highlighted. The other part (Lessons 16 to 50) deals with the various properties of second-order and first- order PDEs. The book emphasizes the applications of PDEs and covers various important topics such as the Hamilton?Jacobi equation, Conservation laws, Similarity solution, Asymptotics and Power series solution and many more. The graded problems, the techniques for solving them, and a large number of exercises with hints and answers help students gain the necessary skill and confidence in handling the subject. Table of Contents Preliminaries. Formulation of Partial Differential Equation. Lagrange Equations. Cauchy Initial Value Problem for Linear First Order Equations. Total Differential Equations (Pfaffian Equations). Generating Integral Surfaces of Lagrange Equation. Orthogonal Surface to a Given System of Surfaces. Compatible System of First Order Equations. Classification of the Solution of First Order Equation. Nonlinear First Order Equations. Integrals of Certain Nonlinear Equations (Standard Forms). Cauchy Initial Value Problem for Nonlinear First O