Definition, Algebra of complex numbers, polar forms, regions, Limits, continuity, differentiability Analyticity, CR equations, Harmonic Functions.
Chapters 1 & 2.
Conformal mappings, bilinear transformations, Special bilinear transformations, fixed points.
Chapter-9 (Sections: 9.1-9.3).
Contour integral, Cauchy-Goursat theorem, Cauchy’s integral formula, winding number, Primitives
Chapter-4 (Sections: 4.1-4.4, 4.7).
Sequences, series, power series, uniform convergence of power series, Taylor’s series, Laurent’s series, Integration and differentiation of Power series.
Chapters- 5 & 6 (Sections: 5.1-5.2, 6.1, 6.3-6.5).
Zeros and singularities of analytic functions, types of singularities, poles, residue theorem.
Chapter-7 (Sections: 7.1-7.3).