Lecture 1 - Introduction
Lecture 2 - Introduction to Complex Numbers
Lecture 3 - de Moivre’s Formula and Stereographic Projection
Lecture 4 - Topology of the Complex Plane - Part-I
Lecture 5 - Topology of the Complex Plane - Part-II
Lecture 6 - Topology of the Complex Plane - Part-III
Lecture 7 - Introduction to Complex Functions
Lecture 8 - Limits and Continuity
Lecture 9 - Differentiation
Lecture 10 - Cauchy-Riemann Equations and Differentiability
Lecture 11 - Analytic functions; the exponential function
Lecture 12 - Sine, Cosine and Harmonic functions
Lecture 13 - Branches of Multifunctions; Hyperbolic Functions
Lecture 14 - Problem Solving Session I
Lecture 15 - Integration and Contours
Lecture 16 - Contour Integration
Lecture 17 - Introduction to Cauchy’s Theorem
Lecture 18 - Cauchy’s Theorem for a Rectangle
Lecture 19 - Cauchy’s theorem - Part-II
Lecture 20 - Cauchy’s Theorem - Part-III
Lecture 21 - Cauchy’s Integral Formula and its Consequences
Lecture 22 - The First and Second Derivatives of Analytic Functions
Lecture 23 - Morera’s Theorem and Higher Order Derivatives of Analytic Functions
Lecture 24 - Problem Solving Session II
Lecture 25 - Introduction to Complex Power Series
Lecture 26 - Analyticity of Power Series
Lecture 27 - Taylor’s Theorem
Lecture 28 - Zeroes of Analytic Functions
Lecture 29 - Counting the Zeroes of Analytic Functions
Lecture 30 - Open mapping theorem - Part-I
Lecture 31 - Open mapping theorem - Part-II
Lecture 32 - Properties of Mobius Transformations - Part-I
Lecture 33 - Properties of Mobius Transformations - Part-II
Lecture 34 - Problem Solving Session III
Lecture 35 - Removable Singularities
Lecture 36 - Poles Classification of Isolated Singularities
Lecture 37 - Essential Singularity & Introduction to Laurent Series
Lecture 38 - Laurent’s Theorem
Lecture 39 - Residue Theorem and Applications
Lecture 40 - Problem Solving Session IV
