COMPUTER ORIENTED NUMERICAL METHODS

Paper Code: 
BCA 401
Credits: 
04
Periods/week: 
04
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.

12.00
Unit I: 

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.

12.00
Unit II: 

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.

12.00
Unit III: 

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.

 

12.00
Unit IV: 

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, Truncation error in interpolation, Spine interpolation(piecewise polynomial).

Numerical Differentiation:- Formulae for Numerical differentiation.

12.00
Unit V: 

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 method, Runge-Kutta Fourth Order Formula, Predictor-Corrector Method(Milne Simpson’s methods, Adams-Bash forth method), 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. 
REFERENCES: 
  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: