Solution of equation - Fixed point iteration: x=g(x) method –
Newton’s method – Solution of linear system by Gaussian elimination and
Gauss-Jordon methods - Iterative methods - Gauss-Seidel methods - Inverse of a
matrix by Gauss Jordon method – Eigen value of a matrix by power method and by
Jacobi method for symmetric matrix.
INTERPOLATION AND APPROXIMATION
Lagrangian Polynomials – Divided differences – Interpolating
with a cubic spline – Newton’s forward and backward difference formulas.
NUMERICAL DIFFERENTIATION AND INTEGRATION
Differentiation using interpolation formulae –Numerical
integration by trapezoidal and Simpson’s 1/3 and 3/8 rules – Romberg’s method –
Two and Three point Gaussian quadrature formulas – Double integrals using trapezoidal
and Simpsons’s rules.
INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single step methods: Taylor series method – Euler methods for
First order Runge – Kutta method for solving first and second order equations –
Multistep methods: Milne’s and Adam’s predictor and corrector methods.
BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL
EQUATIONS
Finite difference solution of second order ordinary differential
equation – Finite difference solution of one dimensional heat equation by explicit
and implicit methods – One dimensional wave equation and two dimensional
Laplace and Poisson equations.
REFERENCE
Text Books
1.VEERARJAN,T and RAMACHANDRAN.T, ‘NUMERICAL MEHODS with
programming in ‘C’ Second Edition Tata McGraw Hill Pub.Co.Ltd, First reprint
2007.
2.SANKAR RAO K’ NUMERICAL METHODS FOR SCIENTISITS AND ENGINEERS
–3rd Edition Princtice Hall of India Private, New Delhi, 2007.
Reference Books
1.P. Kandasamy, K. Thilagavathy and K. Gunavathy, ‘Numerical
Methods’, S.Chand Co. Ltd., New Delhi, 2003.
2.GERALD C.F. and WHEATE, P.O. ‘APPLIED NUMERICAL ANALYSIS’…
Edition, Pearson Education Asia, New Delhi.
