This is a first course in Complex Analysis focussing on holomorphic functions and its basic properties like Cauchy’s theorem and residue theorems, the classification of singularities, and the maximum principle. We shall study the singularities of holomorphic functions. If time permits, we shall also study Branches of the complex logarithm through covering spaces and attempt proving Picard’s theorem.
INTENDED AUDIENCE : Third year Undergraduate or first year Master’s students in various universities.
PREREQUISITES : Real Analysis, Linear Algebra
INDUSTRIES SUPPORT : Almost all engineering-based companies