Learn · A short lecture series on contour integration in the complex plane
Lecture 8 of 27Important theorems in complex variables
Implications of CIF, converse of CG theorem
Prof. Venkata Sonti · IISc Bangalore
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- A short lecture series on contour integration in the complex plane, IISc Bangalore (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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- Tweens profiles and older. How courses are placed
All the lectures
- Introduction to complex variables
- Cauchy Riemann Equations
- Analytic Functions
- Simple definitions
- Definition of sets, domains, theorem on antiderivative
- Cauchy Gorsat Theorem
- Implications of Cauchy Gorsat Theorem, Cauchy Integral Formula
- Implications of CIF, converse of CG theorem
- Examples in contour integrals, ratios of polynomials
- Contour integration of sinc function
- Method of path deformation
- Method of path deformation contd.
- Infinite and finite branch cuts
- Finite Branch Cut.
- Infinite branch cut example
- Contour integration: rectangular contour
- Finite square root branch cut
- Example on finite branch cut
- Pole on a branch cut
- L shaped branch cut
- L shaped branch cut continued
- Inverse Laplace Transform
- Inverse Laplace Transform contd.
- Additional material or corrections to lectures
- Summary of the total course
- Live Session 04-09-2019
- Live Session 24-09-2019