NMCT (B-TECH Civil Engineering 5th)

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.