|

Methodical aspects of approaches to teaching theory of function limits

Authors: Akhmetova F.Kh., Kosova A.V., Pelevina I.N. Published: 30.06.2016
Published in issue: #5(43)/2016  
DOI: 10.18698/2306-8477-2016-5-360  
Category: Technological aspects of the engineering education | Chapter: Pedagogics  
Keywords: Cauchy function limit, Heine function limit, neighborhood of finite and infinite points, evaluation of indeterminate forms

The article discusses some aspects of teaching the theory of limits in the course of mathematical analysis and the problems arising in presenting the educational material. To solve the difficulties in recording the neighborhood of finite and infinite points at different argument tendencies a table is offered that addresses all possible argument tendencies, described through the neighborhoods and intervals, and the Cauchy definitions of the function limit for all cases presented in the table are given. The table summarizing the uncertainties and ways to address them in finding limits of functions is also given. The techniques of calculating all possible limits are illustrated on a wide range of tasks.


References
[1] Ilyin V.A., Poznyak E.G. Osnovy matematicheskogo analiza. V 2 chastyakh. Ch. 1 [Fundamentals of mathematical analysis. In 2 parts. Part 1]. Moscow, Fizmatlit, 2005, 648 p.
[2] Ilyin V.A., Sadovnichiy V.A., Sendov B.Kh. Matematicheskiy analiz. V 2 chastyakh. Ch. 1 [Mathematical analysis. In 2 parts. Part 1]. Moscow, Yurayt Publ., 2013, 660 p.
[3] Morozova V.D. Vvedenie v analiz [Introduction to Calculus]. Moscow, BMSTU Publ., 2014, 408 p.
[4] Piskunov N.S. Differentsialnoe i integralnoe ischislenie. V 2 tomakh. Tom 1 [Differential and Integral Calculus. In 2 volumes. Vol. 1]. Moscow, Integral-Press Publ., 2010, 416 p.
[5] Akhmetova F.Kh., Kosova A.V., Pelevina I.N. Vvedenie v analiz. Teoriya predelov. V 3 chastyakh. Ch. 1 [Introduction to Calculus. Theory of limits. In 3 parts. P. 1]. Moscow, BMSTU Publ., 2014, 33 p.
[6] Akhmetova F.Kh., Efremova S.N., Laskovaya T.A. Vvedenie v analiz. Teoriya predelov. V 3 chastyakh. Ch. 2 [Introduction to Calculus. Theory of limits. In 3 parts. Part 2]. Moscow, BMSTU Publ., 2014, 28 p.
[7] Akhmetova F.Kh., Laskovaya T.A. Pelevina I.N. Vvedenie v analiz. Teoriya predelov. V 3 chastyakh. Ch. 3 [Introduction to Calculus. Theory of limits. In 3 parts. Part 3]. Moscow, BMSTU Publ., 2014, 24 p.
[8] Akhmetova F.Kh., Laskovaya T.A. Pelevina I.N. Nauchno-metodicheskie problemy prepodavaniya teorii beskonechno malykh funktsiy [Scientific and methodical problems of teaching the theory of infinitesimal functions]. Tezisy Mezhdunarodnoy nauchnoy konferentsii "Fiziko-natematicheskie problemy sozdaniya novoy tekhniki " [Abstracts of the International Scientific Conference "Physical and mathematical problems of new technology creation", November 17-19, 2014]. Moscow, BMSTU Publ., 2014, p. 104-105.
[9] Akhmetova F.Kh., Laskovaya T.A. Pelevina I.N. Inzhenernyy vestnik - Engineering Bulletin, 2015, no. 4. Available at: http://engbul.bmstu.ru/doc/773087.html
[10] Akhmetova F.Kh., Laskovaya T.A. Pelevina I.N. Inzhenernyy vestnik - Engineering Bulletin, 2015, no. 5. Available at: http://engbul.bmstu.ru/doc/771171.html