

Errors in Numerical Computation. Their types, analysis and estimation, numerical
instabilities in computation. Solutions to Transcendental and Polynomial
equations. Bisection method, secant method, Regula Falsi
method, Newton Raphson method for polynomial equations. Solutions to System of Linear Algebraic
Equations : Cramers rule, Gauss elimination method, Gauss Jordan method,
Triangularization methods Gauss Siedel method of iteration. Interpolation and Approximation : Linear
interpolation and high order interpolation using Lagrange and Newton
Interpolation methods, finite difference operators and interpolation polynomials
using finite differences. Approximations least square approximation technique,
linear regression. Numerical Differentiation. Methods based on interpolation and finite
differences. Numerical Integration : Trapezoidal rule,
midpoint method, Simpsons 1/3rd and 3/8th rule. Solutions to ordinary differential equations. Taylor series method, Picards method of successive
approximation. Eulers method, Eulers predictor and corrector method. Runge Kutta
method for 2nd and 4th order. Initial and boundary value problems. Numerical Optimisation. Golden section search, Brents method, minimisation
using derivatives, introduction to linear programming 
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