10.5.52 Conformal mappings
Condition: Find a fractional linear function \( \omega(z) \), conformally mapping the domain \( D \) onto the domain \( G \) and satisfying the specified conditions. \[ \begin{array}{l} D=\{|z|>1\}, \quad G=\{|\omega|<2\} \\ \omega(i)=-2, \quad \omega(-2 i)=0 . \end{array}\]
Problems of finding conformal mappings of domains with and without cuts, using linear fractional functions, trigonometric functions, power functions, Zhukovsky function.