NUMERICAL & STATISTICAL METHODS

Computer Arithmetic: Introduction, Floating point representation of numbers, Arithmetic operation with normalized floating point numbers, Consequences of normalized floating point representation of numbers, binary representation of numbers.

Iterative Methods: Introduction, Beginning an iterative method, Method of successive bisection, Method of false position, Newton-Raphson iterative method, Secant method, Method of successive approximation, Comparison of iterative methods.

Solution of simultaneous Algebraic equations: Gauss elimination method, Pivoting, Ill conditioned equations, Refinement of the solution obtained by Gaussian Elimination, Gauss-Seidel Iterative Method, Algorithm to implement Gauss-Seidel method, Comparison of Direct and Iterative Methods.

Interpolation: Theory of interpolation, polynomial forms, difference Table (Forward,   Backward & Divided difference table), Methods of Equal spaced function: - Newton’s forward interpolation, Newton’s Backward interpolation. Methods of unequal spaced function: - Lagrange interpolation, Newton’s Divided difference interpolations.

Numerical Integration: Trapezoidal Rule, Simpson’s rule, Algorithm for Integration of Tabulated Function( Using Trapezoidal rule& Simpson’s rule). Numerical solution of Differential Equations: Euler's method, Euler’s modified method,  Runge-Kutta Fourth Order Formula, Predictor-Corrector Method (Milne Simpson’s methods), Comparison of Predictor-Corrector and Runge-Kutta Methods.