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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, mid-point 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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