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Course11210828527 lectures

A short lecture series on contour integration in the complex plane

Prof. Venkata Sonti · IISc Bangalore

Start with lecture 1 At NPTEL

Lectures

Introduction to complex variables

  1. Introduction to complex variables Video
  2. Cauchy Riemann Equations Video
  3. Analytic Functions Video
  4. Simple definitions Video
  5. Definition of sets, domains, theorem on antiderivative Video
  6. Cauchy Gorsat Theorem Video

Important theorems in complex variables

  1. Implications of Cauchy Gorsat Theorem, Cauchy Integral Formula Video
  2. Implications of CIF, converse of CG theorem Video
  3. Examples in contour integrals, ratios of polynomials Video
  4. Contour integration of sinc function Video
  5. Method of path deformation Video
  6. Method of path deformation contd. Video

Branch cuts of the square root function

  1. Infinite and finite branch cuts Video
  2. Finite Branch Cut. Video
  3. Infinite branch cut example Video
  4. Contour integration: rectangular contour Video
  5. Finite square root branch cut Video
  6. Example on finite branch cut Video

The inverse Laplace transform

  1. Pole on a branch cut Video
  2. L shaped branch cut Video
  3. L shaped branch cut continued Video
  4. Inverse Laplace Transform Video
  5. Inverse Laplace Transform contd. Video
  6. Additional material or corrections to lectures Video
  7. Summary of the total course Video

Live Session

  1. Live Session 04-09-2019 Video
  2. Live Session 24-09-2019 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IISc Bangalore
Department
Mechanical Engineering
Teacher
Prof. Venkata Sonti
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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