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NUMERICAL & STATISTICAL METHODS
This module is designed to help students to know about the concepts of numerical methods and how they are useful in the study of computers.
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.
- Rajaraman, “Computer Oriented Numerical Methods” 3rd Edition, Prentice Hall of India Pvt. Ltd.
- E.Balagurusami, “Numerical Methods” Tata McGraw Hill, 1988.
1. Schaum’s Series, “Numerical Methods”, TMH
2. S.S.Sastry, “Introductory Methods of Numerical Analysis”, second ed., Prentice Hall of -India Pvt. Ltd, 1997.
