10.6.19 Analytic functions
Condition: Restore the analytic function \( f(z) \) in the neighborhood of the point \( z_{0} \) from the known real \( u(x, y) \) or imaginary part \( v(x, y) \) and the value \( f\left(z_{0}\right) \) : \[ v=2 x y-2 y, \quad f(0)=1 \]
Differentiation of analytical functions, finding their real and imaginary parts, finding the number of roots of complex equations using the argument principle, Roucher's theorem and much more in this section.