# Complex Analysis

- Institution: IIT Guwahati
- Department: Mathematics
- Teacher: Prof. P. A. S. Sree Krishna
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111103070)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111103070)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Introduction](https://invisiblenetwork.ai/learn/nptel/111103070/761ab2451732) (Video)
2. [Introduction to Complex Numbers](https://invisiblenetwork.ai/learn/nptel/111103070/5cb6ba516bca) (Video)
3. [de Moivre’s Formula and Stereographic Projection](https://invisiblenetwork.ai/learn/nptel/111103070/4c5b4a412c3c) (Video)
4. [Topology of the Complex Plane Part-I](https://invisiblenetwork.ai/learn/nptel/111103070/f9994265c7d7) (Video)
5. [Topology of the Complex Plane Part-II](https://invisiblenetwork.ai/learn/nptel/111103070/08e2adcba95d) (Video)
6. [Topology of the Complex Plane Part-III](https://invisiblenetwork.ai/learn/nptel/111103070/34700f703492) (Video)
7. [Introduction to Complex Functions](https://invisiblenetwork.ai/learn/nptel/111103070/fc6e05bc84dd) (Video)
8. [Limits and Continuity](https://invisiblenetwork.ai/learn/nptel/111103070/997142279e4b) (Video)
9. [Differentiation](https://invisiblenetwork.ai/learn/nptel/111103070/4830fd6c2b57) (Video)
10. [Cauchy-Riemann Equations and Differentiability](https://invisiblenetwork.ai/learn/nptel/111103070/17f322c4279a) (Video)
11. [Analytic functions; the exponential function](https://invisiblenetwork.ai/learn/nptel/111103070/623293dff43a) (Video)
12. [Sine, Cosine and Harmonic functions](https://invisiblenetwork.ai/learn/nptel/111103070/d8065e4157c4) (Video)
13. [Branches of Multifunctions; Hyperbolic Functions](https://invisiblenetwork.ai/learn/nptel/111103070/14f161b98cc5) (Video)
14. [Problem Solving Session I](https://invisiblenetwork.ai/learn/nptel/111103070/7f1246cc8cc0) (Video)
15. [Integration and Contours](https://invisiblenetwork.ai/learn/nptel/111103070/d010060b6120) (Video)
16. [Contour Integration](https://invisiblenetwork.ai/learn/nptel/111103070/1f8d6a7c9dbf) (Video)
17. [Introduction to Cauchy’s Theorem](https://invisiblenetwork.ai/learn/nptel/111103070/bdebb784cc40) (Video)
18. [Cauchy’s Theorem for a Rectangle](https://invisiblenetwork.ai/learn/nptel/111103070/9d520cebefdb) (Video)
19. [Cauchy’s theorem Part - II](https://invisiblenetwork.ai/learn/nptel/111103070/79fb21717b58) (Video)
20. [Cauchy’s Theorem Part - III](https://invisiblenetwork.ai/learn/nptel/111103070/abbb116e4dbd) (Video)
21. [Cauchy’s Integral Formula and its Consequences](https://invisiblenetwork.ai/learn/nptel/111103070/4efa09198422) (Video)
22. [The First and Second Derivatives of Analytic Functions](https://invisiblenetwork.ai/learn/nptel/111103070/2c30666df0c7) (Video)
23. [Morera’s Theorem and Higher Order Derivatives of Analytic Functions](https://invisiblenetwork.ai/learn/nptel/111103070/dc489314b73e) (Video)
24. [Problem Solving Session II](https://invisiblenetwork.ai/learn/nptel/111103070/913cee87f218) (Video)
25. [Introduction to Complex Power Series](https://invisiblenetwork.ai/learn/nptel/111103070/15d505d9b8db) (Video)
26. [Analyticity of Power Series](https://invisiblenetwork.ai/learn/nptel/111103070/20eae1c8ec70) (Video)
27. [Taylor’s Theorem](https://invisiblenetwork.ai/learn/nptel/111103070/d8a9317263c6) (Video)
28. [Zeroes of Analytic Functions](https://invisiblenetwork.ai/learn/nptel/111103070/81b8b8cf8e07) (Video)
29. [Counting the Zeroes of Analytic Functions](https://invisiblenetwork.ai/learn/nptel/111103070/e848fbca9217) (Video)
30. [Open mapping theorem – Part I](https://invisiblenetwork.ai/learn/nptel/111103070/c602a318b7f0) (Video)
31. [Open mapping theorem – Part II](https://invisiblenetwork.ai/learn/nptel/111103070/e6e8b0ce1744) (Video)
32. [Properties of Mobius Transformations Part I](https://invisiblenetwork.ai/learn/nptel/111103070/8310eeaf8036) (Video)
33. [Properties of Mobius Transformations Part II](https://invisiblenetwork.ai/learn/nptel/111103070/b042e72231d1) (Video)
34. [Problem Solving Session III](https://invisiblenetwork.ai/learn/nptel/111103070/c1835924c19a) (Video)
35. [Removable Singularities](https://invisiblenetwork.ai/learn/nptel/111103070/c9cddf39adb3) (Video)
36. [Poles Classification of Isolated Singularities](https://invisiblenetwork.ai/learn/nptel/111103070/c58b4855db46) (Video)
37. [Essential Singularity & Introduction to Laurent Series](https://invisiblenetwork.ai/learn/nptel/111103070/5cf7eb20978c) (Video)
38. [Laurent’s Theorem](https://invisiblenetwork.ai/learn/nptel/111103070/c7d62eeb5e70) (Video)
39. [Residue Theorem and Applications](https://invisiblenetwork.ai/learn/nptel/111103070/0f38cdc59a7d) (Video)
40. [Problem Solving Session IV](https://invisiblenetwork.ai/learn/nptel/111103070/c360f403eb63) (Video)