Complex Analysis Video Lectures

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