Review of complex numbers, Complex valued functions, Elementary functions(exponential and logarithmic functions, Trigonometric and hyperbolic functions and theirs inverses),

Limits and continuity, 

Applications in Engineering

Derivatives of complex valued functions, Differentiability,

Analyticity, Cauchy Riemann Equations, Harmonic Functions,

Complex integrals, Cauchy-Goursat Theorem, Independence of Path, Cauchy’s Integral Formulas and Their Consequences, Applications

Taylor Series, Laurent Series, Singularities, Zeros and poles, Residue integration method, Residue theorem,

factorization, Tridiagonal solver

Conformal mapping

Linearity, Scaling, First shifting theorem, Heaviside’s Shifting theorem,

Inverse Laplace transformation, Properties of inverse Laplace,

Convolution theorem, Applications in relevant engineering discipline

(Gamma, Beta functions, Periodic functions, Error function),

Fourier Series, Fourier Sine and Cosine series

Fourier transform, Fourier cosine and sine transform, properties.

Applications in relevant engineering discipline

Z-transform, Properties of Z-transform, linearity and scaling, Standard Z transform, Inverse Z-transform

Inverse Z- transform by using residue, convolution theorem of Z-transform,

 Formation of difference equation and its solution using Z-transform.