Calculate Complex Integral using Residue Theorem Part I. Complex Function Theory.

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This Video will explain how to use the Residue Theorem in complex Function Theory using a variety of cuts. Part I.
  1. The Sage of Science
  2. Contour
  3. Cut
  4. Contour Integral
  5. Analytic Function
  6. Complex Analytic Function
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"Complex Variables" by John W. Dettman is a great read: the first part covers the geometry/topology of the complex space from a Mathematician's perspective, and the second part covers application of complex analysis to differential equations and integral transformations, etc. from a Physicist's perspective. For practical reasons, a typical Math Methods for Physics course covers the Cauchy-Riemann Conditions, Conformal Mapping, and applications of the Residue Theorem.

I've used Smith Charts in RF/microwave Engineering for years, but learned from Dettman that the "Smith Chart" is an instance of a Möbius Transformation.

douglasstrother