The importance of the course “Complex Analysis” for me was due to the fact that later on, I was able to apply it’s concepts in order to develop my theorem in “Fluid Dynamics” where there, I explained “The Behavior of Newtonian Fluids in Multiply Connected Domains”.
In this course we first reviewed “Continuous and Holomorphic Functions” on the complex plane and integration along the curves. In the second part we reviewed “Cauchy’s Theorem and it’s applications” especially on evaluation of some integrals. In the third part of the course we reviewed “Meromorphic Functions and the Logarithm” included “Homotopies and Simply Connected Domains”, “The Complex Logarithm” and “Fourier Series and Harmonic Functions”.
Finally in the last part of the course, we learned conformal mappings included “The Schwarz Lemma”, “The Riemann Mapping Theorem” and “Conformal Mappings onto Polygons”.