Unit I
Functions of complex variables : Analytic functions, Harmonic Conjugate, Cauchy-Riemann
Equations, Line Integral, Cauchy’s Theorem, Cauchy’s Integral Formula, Singular Points, Poles
& Residues, Residue Theorem , Application of Residues theorem for evaluation of real integrals
Unit II
Errors & Approximations, Solution of Algebraic & Trancedental Equations (Regula Falsi ,
Newton-Raphson, Iterative, Secant Method), Solution of simultaneous linear equatins by Gauss
Elimination, Gauss Jordan, Crout’s methods , Jacobi’s and Gauss-Siedel Iterative methods
Unit III
Difference Operators, Interpolation ( Newton Forward & Backward Formulae, Central
Interpolation Formulae, Lagrange’s and divided difference formulae ), Numerical Differentiation
and Numerical Integration.
Unit IV
Solution of Ordinary Differential Equations(Taylor’s Series, Picard’s Method, Modified Euler’s
Method, Runge-Kutta Method, Milne’s Predictor & Corrector method ), Correlation and
Regression, Curve Fitting (Method of Least Square).
Unit V
Concept of Probability : Probability Mass function, Probability density function. Discrete
Distribution: Binomial, Poisson’s, Continuous Distribution: Normal Distribution, Exponential
Distribution ,Gamma Distribution ,Beta Distribution ,Testing of Hypothesis |:Students t-test,
Fisher’s z-test, Chi-Square Method
Reference:
(i) Numerical Methods using Matlab by J.H.Mathews and K.D.Fink, P.H.I.
(ii) Numerical Methods for Scientific and Engg. Computation by MKJain, Iyengar and RK
Jain, New Age International Publication
(iii) Mathematical Methods by KV Suryanarayan Rao, SCITECH Publuication
(iv) Numerical Methods using Matlab by Yang,Wiley India
(v) Pobability and Statistics by Ravichandran ,Wiley India
(vi) Mathematical Statistics by George R., Springer
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