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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
& Dividede 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” 3 rd 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:
