# IIT BHU Varanasi Syllabus Ceramic  Numerical Methods

Numerical Methods

Solutions of algebraic and transcendental equations: Graphical method, regula-falsi, Newton-Raphson method,

multiple or near multiple and complex roots. Solution of systems of linear equations, method of elimination, method

of relaxation, iterative methods, ill-conditioned systems.

Interpolation: Absolute, relative, round-off truncation errors, significant digits, estimation of errors, tabulation of a

function, ordinary differences, operators E and subtabulation, divided differences, Aitkons methods, Newton-Cotes

formula, Lagrange’s formula, central differences, formula of gauss, Bessel, Everett. Method of least Squares, cubic

splines.

Numerical Integration: Finite-difference methods, Gaussian quadrature, Eluler-Maclaurin series, asymptotic

expansions. Solution of Ordinary Differential Equations: Series solution, methods of Milne, Adams-Bashforth,

Milne-Simpson multistep and Runge-kutta.

Difference Equations: Numerical solution, relaxation method, solution of ordinary and partial differential equations

by difference method. Numerical solutions of elliptic, parabolic and hyperbolic partial differential equations.