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### Course Title[Course Code]:Operating Systems[CS 513]

Faculty: Computers and Artificial Intelligence

Department: Computer Science

Program: Computer Science

Compulsory / Elective:Elective

Postgraduate(Diploma-First Semester)

Course Description:

This course interdouce some princibles on errors in numerical computation, Machine Computations, Computer Software. Algebraic and Transcendental Equations: Bisection method, Iteration method, Method of False Position, rate of convergence, Method for complex root, Muller’s Method, Quotient Difference method, Newton-Raphson Method. Numerical solution of linear systems, Direct & Iterative methods, Numerical eigenvalue problems. Jacobi, Givens & Householder's method for symmetric matrices, Hessenberg QR iteration. QR- Factoring, LUFactoring, Cholesky (LLT) Decomposition, Singular Value Decomposition. Interpolation: Introduction, Errors in Polynomial interpolation, Finite differences, Decision of errors, Newton’s formula for interpolation, Gauss, Sterling, Bessel’s, Everett’s Formula, Interpolation by unevenly spaced points, Lagrange interpolation formula, Divided Difference, Newton’s General interpolation Formula. Curve Fitting, Cubic Spline & Approximation: Introduction, Method of Least Square curve fitting procedures, fitting a straight line, Curve fitting by sum of exponential, Data fitting with cubic splines, Approximation of functions. Numerical Integration and Differentiation: Introduction, Numerical differentiation, Numerical integration, Trapezoidal rule, Simpson 1/3 rule, Simpson 3/8 rule, Booles & Weddles rule, Euler-Maclariaun formula, Gaussian Formula, Numerical evaluation of singular integrals. Numerical Solution of Ordinary Differential Equations, Related software development.

Department: Computer Science

Program: Computer Science

Compulsory / Elective:Elective

Postgraduate(Diploma-First Semester)

Course Description:

This course interdouce some princibles on errors in numerical computation, Machine Computations, Computer Software. Algebraic and Transcendental Equations: Bisection method, Iteration method, Method of False Position, rate of convergence, Method for complex root, Muller’s Method, Quotient Difference method, Newton-Raphson Method. Numerical solution of linear systems, Direct & Iterative methods, Numerical eigenvalue problems. Jacobi, Givens & Householder's method for symmetric matrices, Hessenberg QR iteration. QR- Factoring, LUFactoring, Cholesky (LLT) Decomposition, Singular Value Decomposition. Interpolation: Introduction, Errors in Polynomial interpolation, Finite differences, Decision of errors, Newton’s formula for interpolation, Gauss, Sterling, Bessel’s, Everett’s Formula, Interpolation by unevenly spaced points, Lagrange interpolation formula, Divided Difference, Newton’s General interpolation Formula. Curve Fitting, Cubic Spline & Approximation: Introduction, Method of Least Square curve fitting procedures, fitting a straight line, Curve fitting by sum of exponential, Data fitting with cubic splines, Approximation of functions. Numerical Integration and Differentiation: Introduction, Numerical differentiation, Numerical integration, Trapezoidal rule, Simpson 1/3 rule, Simpson 3/8 rule, Booles & Weddles rule, Euler-Maclariaun formula, Gaussian Formula, Numerical evaluation of singular integrals. Numerical Solution of Ordinary Differential Equations, Related software development.