Numerical & Statistical Methods

Paper Code: 
GBCA401
Credits: 
06
Periods/week: 
06
Max. Marks: 
100.00
Objective: 

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.

18.00
Unit I: 
Computer Arithmetic

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.

18.00
Unit II: 
Iterative Methods

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.

18.00
Unit III: 
Solution of Simultaneous Algebraic Equations

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.

18.00
Unit IV: 
Interpolation & Methods of Unequal Spaced Function

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.

18.00
Unit V: 
Numerical Integration

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.

ESSENTIAL READINGS: 
  1. Rajaraman, “Computer Oriented Numerical Methods” 3rd Edition, Prentice Hall of India Pvt. Ltd.
  2. E.Balagurusami,  “Numerical Methods” Tata McGraw Hill, 1988.

SUGGESTED READINGS:

  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.
Academic Year: