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# Numerical Computing: Course Outilne

In this course emphasis will be laid, on learning the Numerical methods to solve the Linear, Non-linear Equations, Interpolation and Different Numerical Methods to solve the problems of Integration, Differentiation and Differential Equations

## Course Outline

 Theory Practical Introduction, Number System, Error in Computations & importance of minimizing errors in the context of efficiency, accuracy and stability. Introduction to Matlab, its commands & installation Solution of Non Linear Equation by using Bisection & Regula-Falsi Methods. Variables, Arrays and Matrix declarations Solution of Non Linear Equation by using Iteration & Newton Raphson Methods. Matrix and arrays operation, concatenation Solution of Non Linear Equation by using Muller’s & Graeffe’s Root Squaring Methods. Complex number, Workspace variables Solution of Non Linear Equation by using Graeffe’s Root Squaring Methods. Character string & calling functions Solution of Linear Equation by using Gaussian, Gauss Jordon Elimination Methods and Matrix Inversion. Graphs 2D & 3D plots Solution of Linear Equation by using Crout’s Reduction Methods. Finding roots of polynomials and vice versa Solution of Linear Equation by using Jacobi’s & Gauss-Seidal Iteration Methods. Finding derivative and integral of polynomials Approximation of Eigen Values & Eigen vectors. Solving Bisection method by using Matlab scripts Interpolation & Polynomial Approximation by using Finite Difference Operators. Solving Newton Rophson method by using Matlab scripts Interpolation & Polynomial Approximation by using Newton’s Forward Difference Interpolation Formula. Matlab functions related to Matrices Interpolation & Polynomial Approximation by using Newton’s Backward Difference Interpolation Formula. Matlab functions related to arrays, Implementing Crammer’s Rule Interpolation & Polynomial Approximation by using Lagrange’s Interpolation Formula, Divided Differences. Implementing Gaussian Elimination Method Numerical Differentiation, Numerical integration: Newton-Cotes formulae, trapezoidal rule, Simpson’s formulas, composite rules. Implementing Jacobi Iterative Method Numerical Solution of Ordinary Differential Equations by using Taylor Series & Euler Methods. Implementing Gauss-Seidal Iterative Method Numerical Solution of Ordinary Differential Equations by using Runge-Kutta Method & Predictor Corrector Method Revision