Open AccessDerivative number apparatus and application possibilities
Author(s) -
G. G. Ivanov,
Gennady Alferov,
Vladimir Korolev
Publication year - 2021
Publication title -
vestnik permskogo universiteta. matematika, mehanika, informatika
Language(s) - English
Resource type - Journals
ISSN - 1993-0550
DOI - 10.17072/1993-0550-2021-3-5-18
Subject(s) - smoothness , partial derivative , tangent , differentiable function , frobenius theorem (differential topology) , manifold (fluid mechanics) , mathematics , derivative (finance) , differential (mechanical device) , degree (music) , scope (computer science) , field (mathematics) , pure mathematics , mathematical analysis , computer science , physics , geometry , engineering , curvature , mechanical engineering , scalar curvature , ricci flat manifold , acoustics , financial economics , economics , thermodynamics , programming language
The article develops the apparatus of derived numbers, the use of which allows one to study the behavior of functions of several variables without requiring their differentiability. In addition, the application of this apparatus to the problem of integrability of the field of planes tangent to a differential manifold allows one to generalize the Frobenius theorem and expand its scope by weakening the restrictions on the degree of smoothness of the differential manifolds under consideration. Conditions and criteria for using the apparatus of partial and external derivatives of numbers are proposed.