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February 2025, № 1 (245), pages 74-81

doi: 10.25198/1814-6457-245-74

Gerasimenko S.A., Pavlenko A.N. THE TOPIC “CAUCHY PROBLEM” IN UNDERGRADUATE ENGINEERING FULL-TIME AND PART-TIME EDUCATIONReforming higher education naturally leads to a reduction in the share of classroom studies, which negatively affects the study of disciplines in the mathematical cycle. Thus, there is a need to strengthen the role of independent work of students. It is possible to increase the effectiveness of independent work by using interdisciplinary links with specialized disciplines. For studying the topic “Cauchy Problem for First-Order ODE” by students of engineering programs in full-time and part-time education, we propose a new applied approach, during which the concept of the Cauchy problem is naturally introduced, the meaning of its initial condition is revealed and the main requirements for the problem under consideration and its solution are substantiated. The proposed approach should include a number of necessary stages. To increase the effectiveness of independent work, it is advisable to use the appropriate methodological support. Depending on the direction, it is possible to use methodological instructions, interactive methodological instructions integrated with video files, applications written in various high-level languages, etc. Thus, the study of the topic “Cauchy Problem for First-Order ODE” by students of engineering directions of disciplines should take place in an inseparable unity with the main disciplines of the direction and with the history of engineering and mathematics with the wide application of information technologies.Key words: cauchy problem, ordinary differential equation, applied approach to learning, independent work, information technology, methodology of teaching mathematics in higher education.

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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, №11, p. 98.

2. Petrovsky I.G. (2009) Lectures on the theory of ordinary differential equations: manual for universities. M.: Fizmatlit, 208 p. (Classics and modernity. Mathematics). ISBN 978-5-9221-1144-7.

3. Elsgoltz L.E. (2008) Differential Equations: Textbook. 7th ed. M.: LKI, 309 p. (Classic textbook of Moscow State University). Bibliography: p. 306. Prem. decree.: p. 307-309. ISBN 978-5-382-00638-3.

4. Pontryagin L.S. (1970) Ordinary differential equations: textbook for state universities. 3rd ed., Erased. M.: Nauka, 332 p.: Ill. Prem. decree.: p. 329-331.

5. Vilenkin N.Ya., Dobrokhotova M.A. and Safonov A.N. (1984) Differential equations: textbook. M.: Enlightenment, 176 p.

6. Fedoryuk M.V. (2003) Ordinary differential equations: textbook for universities. 3rd ed., Erased. St. Petersburg: Lan, 448 p. (Textbooks for universities. Special literature). Bibliography: p. 445-447. ISBN 5-8114-0491-3.

7. Popov V.S. and Nikolaev S.A. (1972) General electrical engineering with the basics of electronics. M.: Energy, 504 p.

8. Pisarevsky B.M. and Kharin V.T. (2004) Conversations about mathematics and mathematicians. M.: FIZMATLIT, 208 p. ISBN 5-9221-0418-7.

9. Amelkin V.V. (1987) Differential equations in applications. M.: Science. Main edition of physical and mathematical literature, 160 p.

10. Kiryanov D.V. (2012) Mathcad 15/Mathcad Prime 1.0. St. Petersburg: BHV-Petersburg, 432 p.: Ill. + Video course. ISBN 978-5-9775-0746-2.

11. Arnold V.I. (2011) Mathematical understanding of nature: essays on amazing physical phenomena and their understanding by mathematicians (with drawings by the author). 3rd ed., Stereotype. M.: ICNMO, 144 p. ISBN 978-5-94057-744-7.

12. Andreev V.S. (1982) Theory of nonlinear electrical circuits: textbook for universities. M.: Radio and communications, 280 p., Ill.

13. Gerasimenko S.A., A.N. Pavlenko and O.A. Pikhtilkova (2017) On some aspects of organizing independent work in the disciplines of the mathematical cycle of students of natural sciences. Vestnik of Orenburg State University, № 8 (208), pp. 3-8.

14. Kruchinin V.V. (2004) The use of trees and/or to generate questions and tasks. Bulletin of Tomsk State University, 2004, №284, pp. 183-186.

15. Laptev V.V. and Tolasova V.V. (2010) Generation of task options for laboratory programming. Bulletin of Astrakhan State Technical University. Series: Management, Computing and Computer Science, № 1, pp. 127-131.

16. Zorin Yu.A. (2013) The use of combinatorial generation algorithms in the construction of test task generators. Distance and virtual learning, №6, pp. 54-59.


About this article

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

Year: 2025

doi: 10.25198/1814-6457-245-74

Editor-in-chief
Sergey Aleksandrovich
MIROSHNIKOV

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