Subject Code:  MA5L015 Subject Name:  Partial Differential Equations L-T-P: 3-0-0 Credit: 3
Pre-requisite(s):  Ordinary Differential Equations
Mathematical models leading to partial differential equations. First order quasi-linear equations. Nonlinear equations. Cauchy-Kowalewski’s theorem (for first order). Classification of second order equations and method of characteristics. Riemann’s method and applications. One dimensional wave equation and De’Alembert’s method. Vibration of a membrane. Duhamel’s principle. Solutions of equations in bounded domains and uniqueness of solutions. BVPs for Laplace’s and Poisson’s equations. Maximum principle and applications. Green’s functions and properties. Existence theorem by Perron’s method. Heat equation, Maximum principle. Uniqueness of solutions via energy method. Uniqueness of solutions of IVPs for heat conduction equation. Green’s function for heat equation. Finite difference method for the existence and computation of solution of heat conduction equation.
Text /Reference Books:
  1. Sneddon I. N.  Elements of Partial Differential Equations, McGraw Hill
  2. John F.  Partial Differential Equations, Springer Verlag
Reference Books:
  1. Willams W. E. Partial Differential Equations, Oxford
  2. Strauss W.A. Partial Differential Equations: An Introduction, John Wiley
  3. Folland G. B. Introduction to partial differential equations, Princeton University Press
  4. Rauch J. Partial differential equations, Graduate Texts in Mathematics, 128. Springer-Verlag