AMT 453 2.0 Applied Mathematical Techniques

Course: AMT 111 2.0 Analytical Geometry (Compulsory)

Course content:

First Order partial Differential Equations, Classification,  General first order equation, system of semi-linear first order equations, Quasi-linear equations, Non-linear first order PDEs; Linear Second Order Equations, Classification and reduction to canonical form of linear second order equations; Solution of Cauchy problems for hyperbolic equations by reduction to canonical form,  Well posed problems for partial differential equations;  The wave equation, Energy method and uniqueness; Well posedness  of initial value problem;  The heat equation,  Solutions using Gaussian kernel; uniqueness; maximum principle for heat equation; Laplace’s equation,  Basic properties of harmonic functions; maximum principle for boundary value problem; Existence of solution and well-posedness of boundary value problems for Laplace’s equation; Green’s function ; Duhamel’s Principle;  Nonlinear conservation laws,  Discontinuous solutions of conservation laws; jump condition; model of a traffic flow, uniqueness and the entropy condition.

Recommended Readings:

1. 1. Courant,R., & Hilbert,D. (2008). Methods of Mathematical Physics. John Wiley & Sons.
   2. Strauss,W.A. (2007). Partial Differential Equations: An Introduction. John Wiley & Sons.
   3. Amaranath,T. (2009). An Elementary Course in Partial Differential Equations (2^nd ed). Jones and Bartlett Publishers.
   4. Sneddon,I. (2006). Elements of Partial Differential Equations. Dover Publications.