Complex Numbers, geometric representation, powers and roots of complex numbers. Functions of a complex variable. Analytic functions. Cauchy-Riemann equations. Elementary functions. Conformal mapping (for linear transformation), Contours and contour integration. Cauchy’s theorem, Cauchy integral formula. Power Series, term by term differentiation, Taylor series, Laurent series, Zeros, singularities, poles, essential singularities, Residue theorem and its Applications
Recommended Books:
J. W. Brown and R. V. Churchill, Complex Variables and Applications, McGraw-Hill, 2004.
L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1966