Geodesic
The problem of definition of derivative without invoking the concept of limit
Problemy fiziki, matematiki i tehniki, no. 4 (2010), pp. 24-28.

Voir la notice de l'article provenant de la source Math-Net.Ru

Main theorems about differential functions are proven with the use of the definition of the derivative which does not invoke the concept of limit.
Keywords: derivative, limit, definition, algebra and introduction to calculus.
Mots-clés : calculus 
@article{PFMT_2010_4_a3,
     author = {A. V. Gavriliouk and A. A. Gavriluk},
     title = {The problem of definition of derivative without invoking the concept of limit},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {24--28},
     publisher = {mathdoc},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2010_4_a3/}
}
TY  - JOUR
AU  - A. V. Gavriliouk
AU  - A. A. Gavriluk
TI  - The problem of definition of derivative without invoking the concept of limit
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2010
SP  - 24
EP  - 28
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2010_4_a3/
LA  - ru
ID  - PFMT_2010_4_a3
ER  - 
%0 Journal Article
%A A. V. Gavriliouk
%A A. A. Gavriluk
%T The problem of definition of derivative without invoking the concept of limit
%J Problemy fiziki, matematiki i tehniki
%D 2010
%P 24-28
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2010_4_a3/
%G ru
%F PFMT_2010_4_a3
A. V. Gavriliouk; A. A. Gavriluk. The problem of definition of derivative without invoking the concept of limit. Problemy fiziki, matematiki i tehniki, no. 4 (2010), pp. 24-28. http://geodesic.mathdoc.fr/item/PFMT_2010_4_a3/

[1] Stephen Kuhn, “The Derivative a la Caratheodory”, The American Mathematical Monthly, 98:1 (1991), 40–44 | DOI | MR | Zbl

[2] Ernesto Acosta G., Cesar Delgado G., “Frechet vs. Caratheodory”, The American Mathematical Monthly, 101:4 (1994), 332–338 | DOI | MR | Zbl

[3] S. I. Kalinin, “Ob izlozhenii osnov differentsialnogo ischisleniya veschestvennoznachnykh funktsii odnogo i neskolkikh peremennykh v terminakh ponyatiya differentsiruemosti funktsii po Karateodori”, Matematicheskoe obrazovanie, 2006, no. 2 (37), 18–31

[4] A. V. Gavrilyuk, A. A. Gavrilyuk, “Naglyadnye opredeleniya nepreryvnosti i differentsiruemosti”, Kh Belorusskaya matematicheskaya konferentsiya, Tez. dokl. mezhdunar. nauch. konf. (Minsk, 3–7 noyabrya 2008 g.), v. 1, In-t matematiki NAN Belarusi, Minsk, 2008, 124–125