UPTU SYLLABUS - COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES (MCA-212)

MCA-212: COMPUTER BASED NUMERICAL AND  STATISTICAL TECHNIQUES

Unit-I
Floating point Arithmetic: Representation of floating point numbers, Operations, Normalization, Pitfalls of floating point representation, Errors in numerical computation
Iterative Methods: Zeros of a single transcendental equation and zeros of polynomial using Bisection Method, Iteration Method, Regula-Falsi method, Newton Raphson method, Secant method, Rate of convergence of iterative methods.
Unit-II
Simultaneous Linear Equations: Solutions of system of Linear equations, Gauss Elimination direct method and pivoting, Ill Conditioned system of equations, Refinement of solution. Gauss Seidal iterative method, Rate of Convergence
Interpolation and approximation: Finite Differences, Difference tables
Polynomial Interpolation: Newton’s forward and backward formula
Central Difference Formulae: Gauss forward and backward formula, Stirling’s, Bessel’s, Everett’s formula.
Interpolation with unequal intervals: Langrange’s Interpolation, Newton Divided difference formula, Hermite’s Interpolation
Approximation of function by Taylor’s series and Chebyshev polynomial
Unit-III
Numerical Differentiation and Integration: Introduction, Numerical Differentiation, Numerical Integration, Trapezoidal rule, Simpson’s rules, Boole’s Rule, Weddle’s Rule Euler- Maclaurin Formula
Solution of differential equations: Picard’s Method, Euler’s Method, Taylor’s Method,
Runge-Kutta methods, Predictor-corrector method, Automatic error monitoring, stability of solution.
Unit-IV
Curve fitting, Cubic Spline and Approximation: Method of least squares, fitting of straight lines, polynomials, exponential curves etc
Frequency Chart: Different frequency chart like Histogram, Frequency curve, Pi-chart.
Regression analysis: Linear and Non-linear regression, Multiple regression
Unit-V
Time series and forcasting: Moving averages, smoothening of curves, forecasting models and methods. Statistical Quality Controls methods
Testing of Hypothesis: Test of significance, Chi-square test, t-test, ANOVA, F-Test
Application to medicine, agriculture etc.

References:
1. Rajaraman V., “Computer Oriented Numerical Methods”, PHI
2. Gerald & Wheatley, “Applied Numerical Analyses”, AW
3. Jain, Iyengar and Jain, “Numerical Methods for Scientific and Engineering Computations”, New Age Int.
4. Grewal B. S., “Numerical methods in Engineering and Science”, Khanna Publishers, Delhi
5. T. Veerarajan, T Ramachandran, “Theory and Problems in Numerical Methods”, TMH
6. Pradip Niyogi, “Numerical Analysis and Algorithms”, TMH
7. Francis Scheld, “Numerical Analysis”, TMH
9. Gupta S. P., “Statistical Methods”, Sultan and Sons