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mathematical analysis[¦math·ə¦mad·ə·kəl ə′nal·ə·səs]
the aggregate of all branches of mathematics concerned with the study of functions by infinitesimal methods. Mathematical analysis appeared in systematic form in the works of I. Newton, G. Leibniz, L. Euler, and other mathematicians of the 17th and 18th centuries. A. Cauchy is responsible for substantiating mathematical analysis through the concept of the limit. As used at the present time, the term “mathematical analysis” is more often pedagogical than scientific. A course in mathematical analysis for the mathematical professions as taught in Soviet universities embraces the following: introduction to analysis (function, limit, and continuity), differential and integral calculus, and the theory of series (including power and Fourier series). Concepts from topology and functional analysis are entering more and more into the teaching of mathematical analysis.
REFERENCESVallée-Poussin, C. J. De La. Kurs analiza beskonechno malykh, vols. 1–2. Leningrad-Moscow, 1933. (Translated from French.)
Khinchin, A. Ia. Kratkii kurs matematicheskogo analiza, 3rd ed. Moscow, 1957.
Rudin, U. Osnovy matematicheskogo analiza. Moscow, 1966.
(Translated from English.) Fikhtengol’ts, G. M. Kurs differentsial’nogo i integral’nogo ischisleniia, 6th ed., vols. 1–3. Moscow, 1966.
S. B. STECHKIN