# HAND WRITTEN CLASS NOTES:

Unit 1 Functions of Complex Variable

# Syllabus of Maths 3

NAS 301/NAS 401

Unit – I: Function of Complex variable 8 Analytic function, C-R equations, Harmonic Functions, Cauchy’s integral theorem, Cauchy’s Integral formula, Derivatives of analytic functions, Taylor’s and Laurent’s series, Singularities, Zeroes and Poles, Residue theorem, Evaluation of real integrals of the type ò ò ¥ -¥ f (cos ,sin )d , f (x)dx 2 0 q q q p

Unit – II: Integral Transforms 8 Fourier integral, Complex Fourier transform, Inverse Transforms, Convolution Theorems, Fourier sine and cosine transform, Applications of Fourier transform to simple one dimensional heat transfer equations, wave equations and Laplace equations Z- transform and its application to solve difference equations

Unit – III: Statistical Techniques 8 Moments, Moment generating functions, Skewness, Kurtosis, Curve fitting, Method of least squares, Fitting of straight lines, Polynomials, Exponential curves, Correlation, Linear, non – linear and multiple regression analysis, Binomial, Poisson and Normal distributions, Tests of significations: Chi-square test, ttest

Unit – IV: Numerical Techniques – I 8 Zeroes of transcendental and polynomial equations using Bisection method, Regula-falsi method and Newton-Raphson method, Rate of convergence of above methods. Interpolation: Finite differences, Newton’s forward and backward interpolation, Lagrange’s and Newton’s divided difference formula for unequal intervals.

Unit – V: Numerical Techniques –II 8 Solution of system of linear equations, Matrix Decomposition methods, Jacobi method, Gauss- Seidal method. Numerical differentiation, Numerical integration, Trapezoidal rule, Simpson’s one third and three-eight rules, Solution of ordinary differential equations (first order,second order and simultaneous) by Euler’s, Picard’s and fourth-order Runge- Kutta methods.