Partial Differential Equations : An Introductory Treatment With Applications
Partial Differential Equations : An Introductory Treatment With Applications
 ISBN: 9788120339170
 Author: BHAMRA, K. S.
 Number of Pages: 580
 Availability: In Stock
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About The Book Partial Differential Equations

Book Summary: 
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. This book is recommended in Manipur University, Manipur, Gauhati University, Assam, D.M. College of Science, Manipur. The text is broadly organized into two parts. The first part (Lessons 1 to 15) mostly covers the firstorder 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 secondorder and firstorder PDEs. The book emphasizes the applications of PDEs and covers various important topics such as the HamiltonJacobi 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. Key Features : 1. Presents selfcontained topics in a cohesive style. 2. Includes about 300 workedout examples to enable students to understand the theory and inherent aspects of PDEs. 3. Provides around 450 unsolved problems with hints and answers to help students assess their comprehension of the subject. 
Table of Contents: 
Preface 0 Preliminaries 1 Formulation of Partial Differential Equation 2 Lagrange Equations 3 Cauchy Initial Value Problem for Linear First Order Equations 4 Total Differential Equations (Pfaffian Equations) 5 Generating Integral Surfaces of Lagrange Equation 6 Orthogonal Surface to a Given System of Surfaces 7 Compatible System of First Order Equations 8 Classification of the Solution of First Order Equation 9 Nonlinear First Order Equations 10 Integrals of Certain Nonlinear Equations (Standard Forms) 11 Cauchy Initial Value Problem for Nonlinear First Order Equations 12 System of First Order Equations and Legendre Transformation 13 Linear Equations with Constant Coefficients 14 Discontinuous Solutions of Conservation Laws 15 Transport Problems and Hamiltonian Dynamics 16 Second Order Equations 17 Special Types of Second Order Equations 18 Classification of Second Order Linear Equations 19 Canonical Forms of Second Order Linear Equations 20 Cauchy Initial Value Problem for Second Order Equations 21 Linear Hyperbolic Equations (Riemanns Method) 22 Nonlinear Second Order Equations (Monges Method) 23 Separation of Variables Method 24 Method of Integral Transforms 25 Method of Greens Function 26 Potential Equations 27 Equipotential Surfaces 28 Elliptic Boundary Value Problems 29 Potential Problems in Polar Coordinates 30 Potential Problems by Hankel Transform 31 Potential Problems by Green Function 32 Potential Problems in Polar Coordinates by Green Function 33 Potential Problems in Twodimensional Case by Green Function 34 Potential Problems in Polar Coordinates (Continued) 35 Diffusion Equations 36 Diffusion Problems by Separation of Variables Method 37 Diffusion Problems by Integral Transforms 38 Diffusion Problems by Duhamel Principle and Burgers Equation 39 Diffusion Problems by Green Function 40 Diffusion Problems for Finite Boundary by Green Function 41 Diffusion Problems in One Dimension by Green Function 42 Diffusion Problems for Semiinfinite Domain by Green Function 43 Wave Equations 44 Wave Problems by Separation of Variables Method 45 Wave Problems by Integral Transforms 46 Wave Problems by Duhamel Principle 47 Wave Problems by Green Function 48 Wave Problems in Two Dimension by Green Function 49 Nonlinear Effects in Wave Propagation 50 Perturbation Methods Typical IBVPs in Rectangular Regions Some Wellknown Mathematicians References Index 