Mathematical Analysis

(redirected from Classical analysis)

mathematical analysis

[¦math·ə¦mad·ə·kəl ə′nal·ə·səs]
(analytical chemistry)

Mathematical Analysis


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.


Vallée-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.


References in periodicals archive ?
Stromberg discusses classical analysis that is real in the sense that he does not include any of the Cauchy theory of analytic functions.
Thus, the typically laborious and time-consuming distillation stage required in the classical analysis of volatile acidity is eliminated.
They selected problems to demonstrate techniques that students of classical analysis would need as they move into engineering and physics.
With deep historic roots in classical analysis, the basis of the field lies in the work of Knuth, who put the study of algorithms on a firm scientific basis starting in the late 1960s with his classic series of books.
Classical analysis (gravimetric invasive method) was performed on 6 samples of fresh carp meat.
We compare our results with a previous study, which used classical analysis techniques and reported no main effect.
Marshall teaches us that the American founding points toward intellectual virtue, namely the virtue of prudence or balanced deliberation, and as such, its nobility can be appreciated only if we keep in mind the classical analysis of phronesis.
Readership includes mathematicians, physicists, and engineers interested in geometrical methods in mechanics, assuming a background in calculus, linear algebra, some classical analysis, and point set topology.
The use of obstacle-controlled creep models resolves many anomalies observed in the classical analysis of lead-free solder creep data, including activation energies and power-law exponents that were found to be stress-and/or temperature-dependent.
Working jointly with locomotive-manufacturer EMD, the combination of classical analysis with modern design tools helped achieve thin wall castings with a highly tractive effort.
David Hume [17, 177] perhaps most eloquently states the classical analysis of equilibrium interest rate determination by the interplay of the supply and demand for savings (or capital) rather than money:

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