SECTION-A
Interpolation and curve fitting : Interpolation problem, Lagrangian polynomials,
Divided differences, Interpolating with a cubic spline, Bezier curves and B-spline curves,
Least square approximations.
Non-Linear Equations : Bisection method, Linear Interpolation methods, Newton's
method, Muller's method, fixed-point method.
SECTUIN-B
Simultaneous Linear Equations : Elimination method, Gauss and Gauss-Jordan method,
Jacobi's method, Gauss-Seidal method, Relaxation method.
Numerical Differentiation and Integration : Derivatives from differences tables, Higher
order derivatives, Extrapolation techniques, Newton-cotes integration formula,
Trapezoidal rule, Simpson's rules, Boole's rule and Weddle's rule, Romberg's
Integration.
SECTION--C
Numerical Solution of Ordinary Differential Equations : Taylor series method, Euler
and modified Euler method, Runge-Kutta methods, Milne's method, AdamsMoulton
method, Power method for Eigen values by iteration.
Roots of equation; Graphical methods,Newton Raphson,s methods,Soulation of ordinary
differential equation by Runga Kutta Method. Solution of linear aligebraic equations by
Relaxation Methods
SECTION-D
Numerial Solution of Partial Differential Equations : Finite difference approximations
of partial derivatives, solution of Laplace equation (Standard 5-point formula only),
one-dimensional heat equation (Schmidt method, Crank-Nicolson method, Dufort and
Frankel method) and wave equation.
Numerical Interpolation; Linear and Lagrangian Interpolation .Numerical
intergration.Trapezoidal andSimpson,s Rule. Curve fitting. Linear and polynomial
regression. Curve fitting. Linear and polynomial regression.