Complex Analysis

Juan Carlos Ponce Campuzano, Doug Kuhlmann, Mar 19, 2018

A visual point of view of different topics related to Complex Analysis

Table of Contents

  1. Complex numbers
    1. Roots of a complex number
  2. Mappings
    1. The function f(z)=1/z (Part 1)
    2. The function f(z)=1/z (Part 2)
    3. The function f(z)=z/|z|^2
    4. The function f(z)=sin(z) (Part 1)
    5. The function f(z)=sin(z) (Part 2)
    6. The function f(z)=exp(z)
    7. The function f(z)=log(z) (Part 1)
    8. The function f(z)=log(z) (Part 2)
    9. The function f(z)=log(z+1)
    10. Möbius transformation
    11. Mapping squares
    12. Mapping squares
    13. Mapping squares
  3. Riemann Surfaces
    1. Riemann Surface: z^(1/2)
    2. Riemann Surface: log(z)
    3. Riemann Surface: z^(1/3)
    4. Riemann Surface: (1-z^2)^(1/2)
    5. Riemann Surface: arctan(z)
  4. Analytic functions
    1. Riemann sphere
    2. Riemann sphere (2nd part)
    3. Visualising zeros of complex polynomials
    4. Graphs of complex functions
  5. Series
    1. Series (Part I)
    2. Series (Part II)
    3. The exponential complex function
  6. Applications
    1. Hydrodynamics: Streamlines and velocity potentials
    2. Complex potential

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