The study of various processes leads to the need to clarify (expand) the boundaries of the applicability of computational structures and modeling tools. The purpose of this article is to develop the Taylor expansion for functions of several variables based on the concept of S-differentiability. A function f from L₁Q₀, where Q₀ is an m-dimensional cube, is called S-differentiable at an interior point x₀ of this cube, if there exists an algebraic if there exists an analgebraic polynomial P (x) of degree not greater than first for which it is uniform over all vectors v of the unit sphere Rᵐ the integral of t within 0 and h from the expression f (x₀ + t v) -P (t v) is o (h²) for h 0+. It is shown that with this definition, differentiation of a composite function with a linear interior component is valid, and the vector-gradient principle holds. The following result is proved. Let the function f have continuous partial derivatives up to order n inclusive in some neighborhood of the interior point x₀ Q₀ that are S-differentiable at the point x₀, then the Taylor expansion the function f with accuracy o (x - x₀^n + 1) holds in this neighborhood.
А. Н. Морозов (Wed,) studied this question.