Week  Topics  Study Materials  Materials 
1 
Basic concepts in analysis revisited



2 
Complex Numbers, motivation, basic properties, completeness property.



3 
Continuity of Complex Functions



4 
Differentiation, CauchyRiemann equations, holomorphic functions, Goursat's Lemma,



5 
Power Series, radius of convergence, examples for some complex elementary functions.



6 
Logarithms, cuts and branch points, types of singularities.



7 
Complex Integration



8 
Complex integration, uniform convergence.



9 
Cauchy's Theorem



10 
Cauchy's integral formula, Morera's theorem, fundamental theorem of algebra, Liouville's theorem,



11 
Indefinite Integral theorem, Taylor Series



12 
Applications of Residues.



13 
Laurent series, residue theorem.



14 
Applications of Contour Integration.


