Computer Based Numerical and Statistical Techniques

Program Class: Diploma / B.Sc. CS

Year: II

Semester: IV

Subject: B.Sc. Computer Science

Course Title: Computer Based Numerical and Statistical

Techniques

Course Learning Outcomes:

On completion of this course, learners will be able to:

·       Obtain an intuitive and working understanding of numerical methods for the basic

problems of numerical analysis.

·       Gain experience in the implementation of numerical methods using a computer.

·       Trace error in these methods and need to analyze and predict it.

·       Provide knowledge of various significant and fundamental concepts to inculcate in

the students an adequate understanding of the application of Statistical Methods.

·       Demonstrate the concepts of numerical methods used for different applications.

Credits: 4

Core Compulsory

Max. Marks: –25+75

Min. Passing Marks: 33

Unit

Topics

I

Introduction: Numbers and their accuracy, Computer Arithmetic, 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, Graffe’s method, Rate of convergence of Iterative methods, Polynomial Equations.

II

Interpolation: Finite Differences, Difference tables, Newton’s forward and backward formula

Central Difference Formulae: Gauss forward and backward formula, Stirling’s formula, Bessel’s formula. Laplace Everett’s formula.

Interpolation with unequal intervals: Lagrange’s Interpolation, Newton Divided difference formula, Hermite’s Interpolation,

III

Numerical Integration and Differentiation: Numerical differentiation Numerical Integration: Trapezoidal rule, Simpson’s 1/3 and 3/8 rule, Boole’s rule, Weddle’s rule.

IV

Solution of ordinary differential Equations: Picard’s Method, Euler’s Method, aylor’s Method, Runge-Kutta Methods, Predictor Corrector Methods, and Stability of  olution, some application-based questions on Numerical differentiation and Numerical Integration

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 nonlinear Regression.