Vestnik On-line
Orenburg State University december 23, 2024   RU/EN
Headings of Vestnik
Pedagogics
Psychology
Other

Search
Vak
Антиплагиат
Orcid
Viniti
ЭБС Лань
Rsl
Лицензия Creative Commons

February 2023, № 1 (237), pages 36-42

doi: 10.25198/1814-6457-237-36

Gerasimenko S.A., Pavlenko A.N. ON UNIFICATION OF MULTIPLE, CURVILINEAR AND SURFACE INTEGRALS PRESENTATION IN ENGINEERING DIRECTIONS OF UNDERGRADUATE STUDIESIn modern world, the up-to-date trends in reforming of higher education lead to a significant reduction of classroom activities in the educational process, which extremely negatively affects the study of disciplines of the mathematical cycle due to their abstractness and often complexity of material presentation. Thus, there is a necessity to increase the efficiency of contact work and to widen the role of unsupervised work of students. This problem is especially evident in the study of the topic “Integral calculus for functions of several variables” in the engineering directions of undergraduate studies.
One of the factors that contribute to increasing the efficiency of contact and unsupervised work is the unification of the educational material presentation related to this topic.
In this article, we suggest a new approach to the study of multiple, curvilinear and surface integrals in the engineering directions of undergraduate studies, which include a unified parallel consideration of these integrals when using: 1) a preliminary revision of the topic “Defined integral” and the study of new material on this basis, 2) interdisciplinary connections, 3) information technologies.
It is advisable to use appropriate methodical support to improve the effectiveness of this approach. As the latter, it is appropriate to use tutorials, problem books and individual tasks, posters and 3d models, interactive guidelines integrated with applications, written in high-level languages, generators of typical tasks, etc.
Key words: multiple integrals, curvilinear integrals, surface integrals, methods of mathematics teaching in higher education, interactive methodical support, interdisciplinary connections, contact work, unsupervised work.

Download
References:

1. Mosyagina, N.G. and Shildyaeva, L.V. (2009) Organization of the educational process taking into account the increase in the independent work of students. Successes of modern natural science [Uspekhi sovremennogo estestvoznaniya], № 11, p. 98.

2. Pavlenko, A.N. (2022) On the study of multiple, curvilinear and surface integrals in the engineering directions of the bachelor’s degree. University complex as a regional center of education, science and culture: materials All-Russian. scientific-method. conf. (with international participation) [Universitetskij kompleks kak regional’nyj centr obrazovaniya, nauki i kul’tury: materialy Vseros. nauch.-metod. konf. (s mezhdunar. uchastiem]. Orenburg: OGU, pp. 1370-1374.

3. Fichtenholtz, G.M. (2007) Course of Differential and Integral Calculus [Kurs differencial’nogo i integral’nogo ischisleniya]. M.: Fizmatlit, vol. 1, 680 p. ISBN 978-5-9221-0436-4; Vol. 2 (2006), 864 p. ISBN 978-5-9221-0466-1; Vol. 3 (2008), 728 p. ISBN 5-9221-0737-2.

4. Demidovich, B.P. (2005) Collection of problems and exercises in mathematical analysis: a textbook for universities [Sbornik zadach i uprazhnenij po matematicheskomu analizu: ucheb. posobie dlya vuzov]. M.: AST: Astrel, 560 p. ISBN 5-17-010062-0. ISBN 5-271-03601-4.

5. Berman, G.N. (2002) Collection of problems in the course of mathematical analysis: textbook [Sbornik zadach po kursu matematicheskogo analiza: ucheb. posobie]. 22nd ed., Rev. St. Petersburg: Profession, 432 p. ISBN 5-93913-009-7.

6. Zaporozhets, G.I. (2014) Guide to solving problems in mathematical analysis: textbook [Rukovodstvo k resheniyu zadach po matematicheskomu analizu: uchebnoe posobie]. 8th ed., erased. St. Petersburg: Lan, 464 p. ISBN 978-5-8114-0912-9.

7. Ryabushko, A.P. et al. (2009) Individual tasks in higher mathematics: tutorials. manual. 4Vol. Part 3. Rows. Multiple and curvilinear integrals. Elements of field theory [Individual’nye zadaniya po vysshej matematike: ucheb. posobie. V 4 ch. CH. 3. Ryady. Kratnye i krivolinejnye integraly. Elementy teorii polya]. 5th ed., Ispr. Minsk: Tikhanovskaya. sh., 367 p. ISBN 978-985-06-1677-7.

8. Pavlenko, A.N. and Pikhtilkova, O.A. (2016) Types of Integrals: methodological guidelines for the preparation of reference notes for teachers working with students in higher education programs [Tipy integralov: metodicheskie ukazaniya dlya podgotovki opornyh konspektov dlya prepodavatelej, rabotayushchih so studentami po programmam vysshego obrazovaniya]. Orenburg: OSU, 28 p.

9. Pavlenko, A.N. (2022) Elements of integral calculus for functions of several variables: manual [Elementy integral’nogo ischisleniya dlya funkcij neskol’kih peremennyh: uchebnoe posobie]. Orenburg: OSU, 139 p. ISBN 978-5-7410-2760-8.

10. Nathanson, I.P. (2007) Short course in higher mathematics: a textbook for universities [Kratkij kurs vysshej matematiki: ucheb. posobie dlya vuzov]. 9th ed., erased. St. Petersburg: Lan, 736 p. ISBN 978-5-8114-0123-9.

11. Bermant, A.F. and Aramanovich, I.G. (2005) Short course of mathematical analysis: textbooks for universities [Kratkij kurs matematicheskogo analiza: ucheb. dlya vuzov]. 11th ed., erased. St. Petersburg: Lan, 736 p. (Textbooks for universities. Special literature). ISBN 5-8114-0499-9.

12. Posov, I.A. (2014) Review of generators and methods for generating training tasks. Educational technologies and society [Obrazovatel’nye tekhnologii i obshchestvo], Volume 17, №4, pp. 593-609.

13. Zorin, Yu.A. and Posov, I.A. (2014) Instrumental systems for building and obtaining multivariable test tasks. Computer tools in education [Komp’yuternye instrumenty v obrazovanii], №1, pp. 14-25.

14. Shvetsov, A.N. and Sergushicheva, A.P. (2017) Experience in using the method of automatic generation of test tasks. Educational technologies and society [Obrazovatel’nye tekhnologii i obshchestvo], Volume 20, №4, pp. 318-333.

15. Marek, V.P., Mikushev, S.V., Smirnov, A.G. and Chirtsov, A.S. (2011) Possibilities of using stereoscopic 3D visualization technologies in computer models to support the teaching of physics courses. Computer tools in education [Komp’yutepnye instpumenty v obpazovanii], №2, pp. 39-56.

16. Pavlenko, A.N. (2008) Application of MathCAD mathematical package for quick obtaining of stereoscopic images of various three-dimensional surfaces. Mathematics. Information technology. Education. Collection of scientific works [Matematika. Informacionnye tekhnologii. Obrazovanie. Sbornik nauchnyh trudov]. Orenburg: OSU, 2008. — P. 328-330.


About this article

Authors: Gerasimenko S.A., Pavlenko A.N.

Year: 2023

doi: 10.25198/1814-6457-237-36

Editor-in-chief
Sergey Aleksandrovich
MIROSHNIKOV

Crossref
Cyberleninka
Doi
Europeanlibrary
Googleacademy
scienceindex
worldcat
© Электронное периодическое издание: ВЕСТНИК ОГУ on-line (VESTNIK OSU on-line), ISSN on-line 1814-6465
Зарегистрировано в Федеральной службе по надзору в сфере связи, информационных технологий и массовых коммуникаций
Свидетельство о регистрации СМИ: Эл № ФС77-37678 от 29 сентября 2009 г.
Учредитель: Оренбургский государственный университет (ОГУ)
Главный редактор: С.А. Мирошников
Адрес редакции: 460018, г. Оренбург, проспект Победы, д. 13, к. 2335
Тел./факс: (3532)37-27-78 E-mail: vestnik@mail.osu.ru
1999–2024 © CIT OSU