Introduction to subject complex variables and Fourier series.

Why we need complex numbers?

Definition of Complex Number

lgebraic Properties of Complex Numbers

Complex Variables | Conjugate & Triangle inequality of #complexnumbers

Geometric representation & Modulus of complex numbers

Complex Variables | Polar form of a complex number

Complex Variable | Exponential form

Complex Variable | Proof of Euler's formula

Complex Variables | de Moivre's Theorem

Complex Variables| Roots of Complex numbers

Complex variable | Regions in the Complex plane

Exponential Function

Trigonometric functions

Hyperbolic Functions

Sequence & Series

Functions of a complex variable

Limits of complex Functions

Continuity of Complex functions

Differentiability of Complex Functions

Necessary conditions for differentiable function of Complex variables

Sufficient conditions for differentiable function of complex variables

Analytic function

Harmonic function

Linear transformation

Inversion transformation

Bilinear Transformation

Fixed points of Bilinear transformations

Cross ratio and Bilinear transformation

Special bilinear transformation

The mapping z^2

Conformal mapping

Definition of Fourier Series