Welcome to Department of Mathematics

Mail Us

Call Us

Partial Differential Equations

Code: MA567 | L-T-P-C: 3-1-0-8

Prerequisites: MA541 Real Analysis MA548 ODE

First-Order PDE: Cauchy problem, Method of Characteristics, Lagrange Method, Compatible systems of first-order PDEs, Charpit’s method. Classification of second order PDEs, Canonical Transformations, Characteristics, Canonical forms, characteristics, Propagation of Singularities. Wave Equation: Wave equation in one dimension; Infinite, Semi-infinite, and finite String Problem, D'Alembert's formula, Wave equation in higher dimension; Solutions by spherical means, Inhomogeneous Problems; Duhamel’s principle. Laplace Equation: Fundamental solution, Mean value property, maximum principle, Green's function, Poisson's integral formula, Harnack's inequality, Dirichlet's principle. Heat equation: One dimensional homogeneous heat equation; infinite and semi-infinite rod, Inhomogeneous problems; Duhamel's Principle, Fundamental solution, Maximum principle. Separation of variables: Fourier series expansions, Solutions by separation of Variables method for Wave Equation, Heat Equation and Laplace Equation, BVP in different coordinate systems. Transform methods: Fourier Transforms, Properties of Fourier Transforms, Convolution, Fourier Sine and Cosine Transforms, Application to Initial BVP; Laplace Transforms: Properties of Laplace Transforms, Convolution, Application to initial BVP. Uniqueness ofsolutions of hyperbolic, elliptic, and parabolic equations by Energy Methods.


  1. I. N. Sneddon, Elements of Partial Differential Equations, Dover Publications, 2006.
  2. R. McOwen, Partial Differential Equations: Methods and Applications, Pearson, 2002.


  1. Phoolan Prasad and R. Ravindran, Partial Differential equations, New Age International, 2011.
  2. Qing Han, A Basic Course in Partial Differential Equations, AMS, 2011.
  3. L.C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, 1998
  4. Tyn Myint-U and Lokenath Debnath, Linear Partial Differential Equations for Scientists and Engineers, Birkhauser, 2007.