Applied Mathematics – II Sem 2

Complex Numbers: Cartesian, Polar & Exponential form, De-Moivre's theorem, Hyperbolic functions, Logarithms of Complex numbers

Complex Variables : Cauchy Riemann Equations, , Conformal Mapping and Bilinear Mapping, concept of Line Integral, Riemann Integral, Singularities –Poles, Evaluation of Residues theorem.

Laplace Transform: Introduction, Definition, Properties of Laplace Transform, Laplace Transform of standard function.
Inverse Laplace Transform: Inverse Laplace Transform , Methods of obtaining Inverse Laplace transform, Laplace transform of Periodic Functions, Heavyside Unit-step Function, Dirac-delta function (Unit Impulse Function), Application of Inverse Laplace transform to solve differential equations.

Differentiation under Integral sign, Beta and Gamma Functions, Properties and Duplication Formula, Error Functions

Fourier Series: Fourier Series, Change of Interval, Even and odd functions, Half range
expansions.
Fourier Transform and Inverse Fourier Transform:
Fourier transform of Even and Odd functions, Fourier Transform of sine and cosine functions

Integral Calculus: Double Integral, Area, Triple Integral, Volume