The theory of functions of a real variable (or the theory of functions of a real variable ) is a section of analysis aimed at an in-depth study of two concepts of “classical” mathematical analysis : derivative and integral [1] .
Some of the facts that are now part of the theory of functions of a real variable were discovered back in the 19th century, but they could not be explained in the framework of the “classical” analysis [2] . For example, such facts included the Weierstrass function proposed by the German mathematician Karl Weierstrass , which is continuous but has no derivative at any point [1] [3] .
Thus, the theory of functions of a real variable develops the results of the “classical” mathematical analysis and generalizes its concepts, being, as it were, the next stage in the development of analysis in its current broad sense [2] .
Among the achievements of the theory of functions of a real variable was the creation by the French mathematician Henri Lebesgue at the turn of the 20th century of a coherent theory of integration [1] [3] . In particular, all modern mathematical physics relies on his theory of integration [1] .
Tutorials
- Natanson, I.P. Theory of functions of a real variable. - M .: Nauka, 1974.- 484 p.
- Rudin U. Fundamentals of mathematical analysis. M., 1976
See also
- The theory of functions of a complex variable - TFVP (theory of functions of a real variable) and TFKP (theory of functions of a complex variable) form a theory of functions [3] .
- Functional analysis
Notes
- ↑ 1 2 3 4 Man is a sign system . - Young Guard, 1988. - “Mathematical analysis in the narrow sense includes the theory of functions of a real variable, the theory of functions of a complex variable, harmonic analysis and functional analysis.
The theory of functions of a real variable is engaged in an in-depth study of the fundamental concepts of classical analysis - a derivative and an integral. The famous example of continuous function belongs to it (K. ".
Mathematician (mathematical analysis and its applications). E. M. Dynkin (1988 - - World of professions. Man is a sign system) . - ↑ 1 2 V D Pogrebnaya. THEORY OF FUNCTIONS OF A VALID VARIABLE. LECTURE INSPECTORATE (PDF) . Sumy, Sumy State University : MINISTRY OF EDUCATION AND SCIENCE, YOUTH AND SPORTS OF UKRAINE, SUMI STATE UNIVERSITY.
- ↑ 1 2 3 FUNCTIONS THEORY . Encyclopedia Round the world .