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Introduction:
Errors in Numerical Computation, Mathematical Preliminaries, Errors and their Analysis, Machine Computations, Computer Software.
Algebraic & Trancedental Equation:
Bisection Method Iteration Method, Method of False Position, Rate of Convergence, Method for Complex Root, Mullers Method, Quotient difference Method, Newton-Raphson Method.
Interpolation:
Introduction, Errors in Polynomial Interpolation, Finite Differences, Decision of Errors, Newton’s formulae for Interpolation, Gauss, Stirling, Bessels’s, Everett’s Formulae, 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 Exponentials, Data Fitting with Cubic Splines, Approximation of Functions.
Numerical Integration & Differentiation:
Introduction, Numerical differentiation, Numerical Integration, Trapezoidal Rule, Simpson 1/3 rule, Simpson 3/8 Rule, Booles and Weddles rule, Euler- Maclariaun Formula, Gaussian formula Numerical Evaluation of Singular Integrals.
Statistical Computation:
Frequency Chart, Regression analysis, Least Square fit, Polynomial fit, Linear & Non Linear Regression, Multiple Regression, Statistical Quality Control Methods.
Text Books & References:
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