الفهرس 
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Abstract
This dissertation seeks an approximate analytical solution of the Dirichlet problem for the two-dimensional Laplace equation in complex simply or multiply connected domains with smooth boundaries by a method based on the essential application of complex analysis. And the approximate analytical solution of the Neumann problem for the two-dimensional Laplace equation in complex simply connected domains with smooth boundaries. An approximate analytical solution is found by reducing the problem to the Fredholm integral equation of the second kind for boundary values of the conjugate harmonic function. The approximate solution of the integral equation has the form of truncated Fourier series, and we obtain the coefficients by solving the truncated finite linear system of equations. An accuracy assessment of the obtained approximate solution is given. Finally, the solution of the two-dimensional Dirichlet problem is the real part of the Cauchy integral. The presence of the Cauchy integral the analytic function - that allows us to use the analytic continuation to calculate the solution at points arbitrarily close to the boundary.