Calculus of variations – Euler’s Equation – Variation problems in parametric form – Natural Boundary condition; Maxima & Minima

Field of externals – Conditional extreme –Direct methods Raleigh - Ritz method – Galerkin’s method -Euler’s finite difference method

Kanterrich method;Integral Equations – Relation to a system of algebraic equations – Fredholm equation – Method of successive approximation – Volterra equation – Boundary value problems

Finite difference scheme for elliptic, Parabolic and hyperbolic partial differential equations.

Introduction to Finite element method – Rules for forming interpolation function – Shape function – Application to Fluid flow and heat flow problems.


1) Grewal, B.S., “Higher Engineering Mathematics”, 36th Edition, Khanna

Publishers, 2001

2) Gupta, S.C., and Kapoor, V.K., “Fundamentals of Mathematical Statistics”, SultanChand & Sons, 1981

3) Kreyszig, E. “Advanced Engineering Mathematics”, Khanna Publishers, 1996