Numerical & Statistical Methods (Theory)

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.

NOTE:

Problem will be solved by using Scientific Calculators (Non Programmable). Candidates must know about all functions and operations of scientific calculator.