MCA-105 Computer Oriented Numerical and Statistical Methods

Note:Examiner will be required to set NINE questions in all. Question Number 1 will consist of total 8 parts (objective type/short-answer type questions) covering the entire syllabus and will carry 24 marks. In addition to the compulsory question there will be four units i.e. Unit-I to Unit-IV. Examiner will set two questions from each Unit of the syllabus and each question will carry 14 marks. Student will be required to attempt FIVE questions in all. Question Number 1 will be compulsory. In addition to compulsory question, student will have to attempt four more questions selecting One question from each Unit.

Total Marks : 100  Theory Paper : 80  Internal Assessment: 20

Time : 3 Hours

Unit-I

Computer Arithmatic: Floating-point representation of numbers, arithmetic operations with normalized floating point numbers and their consequences. Error in number representation - pitfalls in computing.

Iterative Methods: Bisection, False position, Newton-Raphson methods, Discussion of convergences, Graeffe’s Root Squaring Method and Bairstow's Method.

Unit-II

Solution of Simultaneous Linear Equations and ordinary Differential Equations: Gauss elimination method, Ill-conditioned equations, Gauss-Seidal iterative method, Euler method, Euler’s Modified Method, Taylor-Series Method, Runge-Kutta method, Predictor-Corrector methods.

Numerical Differentiation and Integration: Differentiation formulae based on polynomial fit, Pitfalls in differentiation, Trapezoidal, Simpson's rules and Gaussian Quadrature.

Unit-III

Interpolation and Approximation: Polynomial interpolation, Difference tables, Inverse interpolation, Polynomial fitting and other curve fitting. Approximation of functions by Taylor series and Chebyshev polynomials.

Unit-IV

Statistical methods: Sample distributions, Test of Significance: Chi-Square Test, t and F test.

Analysis of Variance: Definition, Assumptions, Cochran's Theorem (only statement), One-way classification, ANOVA Table, Two-way classification (with one observation per cell).

Time Series Analysis: Components and Analysis of Time Series, Measurement of Trend, Seasonal fluctuations and cyclic movement.

References :

• Gupta S.P. and Kapoor, V.K., Fundamentals of Applied statistics, Sultan Chand & Sons.
• Gupta S.P. and Kapoor, V.K., Fundamentals of Mathematical Statistics, Sultan Chand and Sons.
• Rajaraman V., Computer Oriented Numerical Methods, Prentice Hall, India.
• Graybill, Introduction to Statistics, McGraw.
• Anderson, Statistical Modelling, McGraw.
• M.K.Jain, S.R.K. Iyengar and R.K.Jain, Numerical Methods for Scientific and Engineering Computation.
• H.C.Saxena, Finite Differences and Numerical Analysis.
• Modes A., Numerical Analysis for Computer Science.