Unit –I :
Computer Arithmetic and Errors: Floating Point Arithmetic, Machine epsilon, Round off Error,
Chopping Error, Truncation Error, Associative and Distributive Law in Floating Point arithmetic, Inherent
Error, Error propagation, Numerical Instability
Roots of Equation: Secant Method, Newton Raphson Method and Fixed point Iteration Methods for
Simple roots and derivation of their rate of convergence, Aitken Acceleration of Convergence, Modified
Newton Raphson Method for Multiple roots, Birge-Vieta Method for Polynomials, Bairstrow Method for
quadratic factors, Computer Algorithms of these methods.  Unit –II
Interpolation: Algorithms and Error Analysis of Lagrange and Newton divided difference interpolations,
Relationship in various difference operators, Piecewise Linear Interpolation, Cubic Spline Interpolation,
Natural Spline, Chebshev Polynomial Approximations, Lanczos Economization of Power Series
Curve fitting: Linear and Non Linear Least Squares Approximation, ill Conditioning in Least Squares
Methods, Gram-Schmidt Process of Orthogonalization. Computer Algorithms of Least Square Curve Fitting
 Unit – III
Differentiation: Methods based on Interpolation and Finite Differences, Richrdson Extrapolation
Integration: Error Analysis of Trepezoidal and Simpson Methods, Newton Cotes Integration Methods,
Guassian Integration Methods: Guass Legendre Method, Lobatto Integration Method and Radau Integration
Method, Error Terms in Integration Methods 
Unit – IV
Solution of Simultaneous Linear Algebraic Equations: Guass Elimination Method, ill Conditioned
Systems, Condition Number, Successive Over Relaxation Method, Rate of Convergence
Solution of Ordinary Differential equations: Single Step Methods-Runge-Kutta Second Order, Third
Order and Fourth Order Methods, Multi Step Method-Predictor- Corrector Method
Statistical Techniques: Statistical Hypotheses, Test of Hypotheses, Type-I and Type-II Errors, Level of
Significance, Test involving Normal Distribution