AMAT 41204

>< Type/ Status : Core
>< Title : Boundary Value Problems
>< Pre-requisites : PMAT 41024
>< Objectives :
At the end of this course, the student will be familiar with two dimensional and three-Dimensional cases of second order linear partial differential equations and their applications.
>< Course Content :

Partial Differential Equations in two variables: Linear second-order equations in two independent variables, Normal forms, Hyperbolic, parabolic and elliptic equations, Boundary value problems in rectangular and cylindrical coordinates, Applications to heat flow, Vibrations and waves, Laplace and poisson equations in two dimensions, Bessel functions.

Boundary Value Problems in Three Dimensions: Green's theorem in three dimensions, Uniqueness of solutions with Dirichlet and Neumann boundary conditions, Formal solutions of boundary value problems in electrostatics, Method of images, Laplace equation in spherical polar coordinates, Boundary value problems with spherical symmetry; Heat and wave equations, Three dimensional boundary value problems with azimuthal symmetry, Legendre functions and applications to gravitation and electrostatics, Potentials of circular rings and discs.

>< Methodology :A combination of lectures, tutorial discussions and presentations
>< Scheme of Evaluation : Based on tutorials, presentations and end of course examination
>< Recommended Reading :
1. Habernsann, R. (1987). Elementary Applied Partial Differential Equations, Prentice-Hall.
2. Raisinghania, M.D. (1991). Ordinary and Partial Differential Equations, S. Chands, India.

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