Training Manual . — Vladivostok: FEFU, 2010. — 120 s. The basic concepts of the method of finite differences of sampling of differential equations of mathematical physics. are presented. Examples of its application in the sampling of initial boundary problems for both ordinary differential equations and the following partial differential equations: transport equations, one-dimensional thermal conductivity equation, one-dimensional wave equation, and two-dimensional Poisson equation. Particular attention is paid to the construction of cost-effective difference schemes of increased and maximum accuracy on a given pattern of the difference grid. The manual is intended for students of mathematical and natural specialties .