10.6.21 Analytic functions
condition: Recover the analytic function \( f(z) \) in a neighborhood of the point \( z_{0} \) from the known real \( u(x, y) \) or imaginary part \( v(x, y) \) and the value \( f\left(z_{0}\right) \). \[ u=e^{-y} \cos x+x, f(0)=1 \]
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.