Computer Oriented Numerical and Statistical Techniques

Paper Code: 
MCA 423
Credits: 
04
Periods/week: 
04
Max. Marks: 
100.00
Objective: 
  • To enable students to obtain an intuitive and working understanding of numerical methods for the basic problems of numerical analysis. 
  • To gain an experience in the implementation of numerical methods using a computer.
  • To make students acquainted to trace error in these methods and need to analyze and predict it.
  • To Discuss various significant and fundamental concepts to inculcate in the students an adequate understanding of the application of Statistical methods.
12.00
Unit I: 
Solution of Non Linear equations:

Introduction to linear and non linear equations, measures of accuracy, Bisection Method, Iteration Method, Regula-Falsi method, Newton Raphson method, Rate of convergence of iterative methods.

Solutions of system of Linear equations-  Direct Method - Gauss Elimination method  and pivoting, Ill Conditioned system of equations. Iterative method- Gauss Seidal Method.

12.00
Unit II: 
Interpolation and Approximation:

Finite Differences, Difference tables, Newton’s forward and backward formula, Central Difference Formulae: Gauss forward and backward formula.

Interpolation with unequal intervals: Langrange’s Interpolation, Newton Divided difference formula.

10.00
Unit III: 
Numerical Integration:

Trapezoidal rule, Simpson’s rules.

Solution of Differential Equation: Range kutta methods; Predictor-Corrector methods.

13.00
Unit IV: 
Statistical Computation:

Frequency charts: Different frequency charts.

Regression Analysis : Curve fitting and Approximation: Method of least squares, fitting of Linear Function, fitting of Nonlinear Function- polynomials, exponential curves .

Linear regression and Nonlinear regression Algorithms; Multiple regression Algorithms

13.00
Unit V: 
Time Service and Forecasting:

Moving averages, Smoothening of curves: Forecasting models and methods. 
Statistical Quality control Methods: Test of significance: Chi-square test, F-Test, t- test, Factor Analysis, ANOVA, Applications to medicine, psychology etc. 

ESSENTIAL READINGS: 

1. Balaguruswami, E., 2000 : Computer Oriented Statistical and Numerical Methods, Mac.Million

2. J.K Sharma,A.M Natarajan,P.Balasubramani and A. Tamilarasi 2013 1st edition : Statitical and  Quantitative Methods

REFERENCES: 

1.  Salaria, R.S. : Computer Oriented Numerical Methods, Khanna Book Publishing Co. (P.) Ltd., New Delhi. 5th edition 2012

2.  P. Thangaraj :Computer oriented Numerical Methods PHI learning , Second Edition 2010

3. Rajaraman, V., 1980 : Computer Oriented Numerical Methods, 3rd Ed., Prentice Hall, India.

Academic Year: 
2017-18
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