MATHEMATICSIII:

 Unit  I : Integral Transforms
Fourier integral, Fourier complex transform, Fourier sine and cosine transforms and applications to simple heat transfer equations.
Z – transform and its application to solve difference equations.
 Unit  II : Functions of a Complex Variable  I
Analytic functions, CR equations and harmonic functions, Line integral in the complex plane, Cauchy's integral theorem, Cauchy's integral formula for derivatives of analytic functions, Liouvilles theorem, Fundamental theorem of algebra.
 Unit  III : Functions of a Complex Variable  II
Representation of a function by power series, Taylor's and Laurent's series, Singularities, zeroes and poles, Residue theorem, evaluation of real integrals of type
f (cosq, sinq) dq and f (x) dx, Conformal mapping and bilinear transformations
 Unit  IV : Statistics and Probability
Moments, Moment generating functions, Skewness, Kurtosis,Correlation and Regression, Binomial distribution, Poisson distribution, Normal distribution.
 Unit  V : Curve Fitting and Solution of Equations
Method of least squares and curve fitting of straight line and parabola, Solution of cubic and biquadratic equations
