Partial Differential equations – basic concepts – One dimensional heat flow equation - Two dimensional heat flow equation in steady flow in Cartesian and Polar coordinates.
Calculus of variations - Euler's equation - Variational problems in parametric form - Natural boundary condition – Conditional Extremum - Isoperimetric problems.
Numerical Solution of ODE’s – Euler’s, Taylor’s and Runge Kutta methods – Milne’s and Adams’ predictor-corrector methods.
Finite difference scheme for elliptic, parabolic, and hyperbolic partial differential equations.
Introduction to Finite Element Method - Rules for forming interpolation functions - Shape functions - Application to fluid flow and heat transfer problems.
1. Desai, C.S. and Abel, J. P., Introduction to Finite Element Method, Van Nostrand Reinhold.
2. Elsegolts, L., Differential Equations and the Calculus of Variations, Mir Publishers.
3. Grewal, B.S., Higher Engineering Mathematics, Khanna Publishers.
4. Reddy, J.N., Introduction to Finite Element Method, Mcgraw Hill.
