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