Complex Analysis


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