Computer Programming and Numerical Analysis

 

Part-I: Computer Programming

 

Algorithm and programs: Problem analysis and development of algorithms. Program coding, execution, design, validation and refinement.

Basic FORTRAN: Data type, operations functions, assignment statement, input-output, stop and end statement.

Control structure: Logical data type, logical if and block if, do and continue, Go to statement, While statement.

Input-output: formatted input and output, File processing.

Dimensional arrays: Arrays and subscripted variables, dimension statement, parameter and data statement, examples average group data, sorting and searching.

Multidimensional arrays: Matrix operations, Solving linear system, Functions and subroutines: Library functions and statement functions, function subprogram, subroutine, subprogram, Common statement. 

 

Part-II: Numerical Analysis

 

Solutions of equations of one variable: Bisection method, Fixed point iteration, Newton-Raphson method, Error analysis for iterative method.

Interpolation and polynomial approximation: Taylor polynomials, Interpolation and Lagrange polynomial, Iterated interpolation.

Numerical differentiation & integration: Numerical differentiation with backward – difference formula, forward difference formula, Adaptive quadrature method, Trapezium method, Simpson method, Matrix algebra and system of equations. Matrix operations, Gauss-Jordan elimination method. SOR Method. (Successive over-Relaxation method).