[CA/Week 6] 2. Integrals with power-type integrand and two branch points, Part II.

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Week 6 of the course "Complex Analysis" is dedicated to integrals with multivalued functions.
Topics of the course:

1. Algebra of complex numbers. Differentiation and integration in a complex plane.
2. Singularities of functions of complex variables.
3. Contour integration. Residue theory. Jordan's lemma.
4. Multivalued functions and regular branches
5. Analytical continuation and Riemann surfaces.
6. Integrals with multivalued functions.
7. Gamma function and its applications.
  1. Stokes-Line
  2. Complex Analysis
  3. Integrals
  4. multivalued functions
  5. branch points
  6. branch cuts
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Комментарии
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At 2:44, how do we pick which Integral is to be designated as I ? since both of them could be chosen as I, and the other one could be expressed in terms of the first one ?

gauravojha
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Looks great, keep up the amazing work!

ytzenon
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The same arrow method for calculation of arg (f(z)) applied to int_0^3 x^(3/4) (3-x)^(1/4) / (5-x) dx doesn't work! You will get delta arg(f(z)) = -2 pi instead of 2 pi.

FunctionalIntegral