GBTU CBNST syllabus

TAS-302

COMPUTER BASED NUMERICAL AND STATISTICAL TECHNIQUES

L T P

3 1 0

Unit-I

Introduction:

Numbers and their accuracy, Computer Arithmetic, Mathematical

preliminaries, Errors and their Computation, General error formula, Error in a series

approximation

Solution of Algebraic and Transcendental Equation:

Bisection Method, Iteration method, Method of false position, Newton-Raphson method,

Methods of finding complex roots, Muller’s method, Rate of convergence of Iterative

methods, Polynomial Equations.

Unit-II

Interpolation:

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,

Unit-III

Numerical Integration and Differentiation:

Introduction, Numerical differentiation

Numerical Integration: Trapezoidal rule, Simpson’s 1/3 and 3/8 rule, Boole’s rule,

Waddle’s rule.

Unit-IV

Solution of differential Equations:

Picard’s Method, Euler’s Method, Taylor’s Method,

Runge-Kutta Methods, Predictor Corrector Methods, Automatic Error Monitoring and

Stability of solution

Unit-V

Statistical Computation:

Frequency chart, Curve fitting by method of least squares,

fitting of straight lines, polynomials, exponential curves etc, Data fitting with Cubic

splines, Regression Analysis, Linear and Non linear Regression, Multiple regression,

Statistical Quality Control methods.

References:

1. Rajaraman V, “Computer Oriented Numerical Methods”, Pearson Education

2. Gerald & Whealey, “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

8. Sastry S. S, “Introductory Methods of Numerical Analysis”, Pearson Education.

9. Gupta C.B., Vijay Gupta, “Introduction to Statistical Methods”, Vikas Publishing.

10. Goyal, M, “Computer Based Numerical and Statistical Techniques”, Firewall

Media, New Delhi.