Computer Based Numerical & Statistical Techniques

Unit No.

CONTENT

1

Floating point Arithmetic ⇗:

• Representation of floating point numbers, Operations, Normalization, Pitfalls of floating point representation, Errors in numerical computation Iterative Methods: Solution of Algebric and Transcendental Equation using Bisection Method, Iteration Method, Regula-Falsi method, Newton Raphson method, Secant method (Only Solutions to be included no proofs are required).

2

Simultaneous Linear Algebric Equations ⇗:

• Matrix Inversion Method, Gauss Elimination method , ILL Conditioned system of equations. Finite Differences , Interpolation and approximation: Finite Differences, Difference tables(Forward and Backward),Shift Operator E 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. (Only Solutions to be included no proofs are required).

3

Numerical Integration ⇗:

• Differentiation using Newton Forward and Newton Backward Formula. Numerical Integration: Trapezoidal rule, Simpson’s rules, Boole’s Rule, Weddle’s Rule.

Solution of differential equations ⇗:

• Picard’s Method, Euler’s Method, Modified Euler’s Method Taylor’s Method, Runge-Kutta methods (Only Solutions to be included no proofs are required).

4

Curve fitting, Cubic Spline and Approximation ⇗:

• Method of least squares, fitting of straight lines, polynomials, Exponential curves.

Statistical Computation:

• Frequency Distribution, Cumulative, Relative Frequency distribution, Graphical Representation of Frequency Distribution.

Regression analysis

• Linear and Non-linear regression, Multiple regression.

Correlation Analysis

• Karl Pearson, Rank Correlation, Spearman Coefficent.

5

Time series and forecasting ⇗:

• Measurement of secular trend methods, forecasting models and methods.