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. 
  • Gain an experience in the implementation of numerical methods using a computer.
  • Trace error in these methods and need to analyze and predict it.
  • Have an adequate understanding of the application of Statistical methods.
12.00
Unit I: 
Solution of Non Linear equations

Introduction to linear and nonlinear 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: Runge 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: Factor Analysis, ANOVA, Test of significance: Xtest and F-test Applications to medicine, psychology etc.

ESSENTIAL READINGS: 
  • Balaguruswami, E., “Computer Oriented Statistical and Numerical Methods”, Mac. Million, 2000.
  • C.R Kothari, “Research Methodology (Methods and Techniques)”, New Age International, 2009.
REFERENCES: 
  • Salaria, R.S., “Computer Oriented Numerical Methods”, Khanna Book Publishing Co. (P.) Ltd., New Delhi. 5th edition 2012.
  • Rajaraman, V., “Computer Programming in C”, Prentice Hall of India, 2004.
  • Krishnanmurthy E.V. & Sen S. K., “Computer Based Numerical Algorithms”, East West Press, 1976.
  • Rajaraman, V, “Computer Oriented Numerical Methods”, 3rd edition, Prentice Hall, 2004.
  • J.K Sharma, A.M Natarajan, P.Balasubramani and A. Tamilarasi, “Statistical and Quantitative Methods”, 2013.
Academic Year: 
2018-19
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