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.
REFERENCES
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
