INTEGRATION OF INTERDISCIPLINARY SCIENTIFIC KNOWLEDGE IN TEACHING INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS
- Autores: Kornilov V.S.1
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Afiliações:
- Moscow city pedagogical university
- Edição: Volume 15, Nº 3 (2018)
- Páginas: 304-318
- Seção: INNOVATION PEDAGOGICAL TECHNOLOGIES IN EDUCATION
- URL: https://journal-vniispk.ru/2312-8631/article/view/333543
- DOI: https://doi.org/10.22363/2312-8631-2018-15-3-304-318
- ID: 333543
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Resumo
Problem and goal. In the process of teaching students inverse problems for differential equations, one of the important goals is to form students ‘ fundamental knowledge in the field of inverse problems, in the field of applied and computational mathematics; to develop mathematical creativity that allows students after graduation, working in research institutions, to successfully solve a variety of complex mathematical problems in the implementation of practical applied research. Methodology. In the process of teaching students inverse problems for differential equations, the system of humanitarian-oriented training sessions is designed, the methods of rational reasoning are used, an individual approach to learning is implemented. Results. Humanitarian-oriented training sessions on inverse problems for differential equations are aimed at creating situations that require students, according to the results of solving the inverse problem, to make logical conclusions of applied and humanitarian character, to overcome moral contradictions, to make a reasonable choice of the right position in society. The skills and experience gained in the course of training in the application of rational reasoning in the study of inverse problems for differential equations allow students not only to effectively investigate applied problems, but also to form fundamental knowledge in the field of applied mathematics. Individual approach in teaching inverse problems for differential equations acts as a didactic principle of training, education and development of students, taking into account the personal characteristics of students, the level of intellectual development, cognitive interests and other factors that affect the success of learning. Conclusion. Humanitarian-oriented training sessions on inverse problems for differential equations, methods of rational reasoning, individual approach to learning allows the students to form a system of fundamental knowledge in inverse problems for partial differential equations, integrating multidisciplinary scientific knowledge, to identify humanitarian and scientific-educational potential of such learning, to justify the positive contribution of teaching inverse problems for differential equations in humanization and fundamentalization of mathematical education.
Sobre autores
Viktor Kornilov
Moscow city pedagogical university
Autor responsável pela correspondência
Email: vs_kornilov@mail.ru
doctor of pedagogical sciences, candidate of physical and mathematical sciences, full professor, deputy head of the department of informatization of education of the Moscow city pedagogical university
29, Sheremetyevskaya str., Moscow, 127521, Russian FederationBibliografia
- Agranovich Z.S., Marchenko V.A. Obratnaya zadacha teorii rasseyaniya [the inverse problem of scattering theory]: monografiya. Har’kov: Izd-vo Har’kovskogo universiteta, 1960. 268 p.
- Anikonov YU.E., Pestov L.N. Formuly v linejnyh i nelinejnyh zadachah tomografii [Formulas in linear and nonlinear tomography problems]: monografiya. Novosibirsk: NGU, 1990. 64 p.
- Belishev M.I., Blagoveshchenskij A.S. Dinamicheskie obratnye zadachi teorii voln [Dynamic inverse problems of wave theory]: monografiya. SPb.: SpbGU, 1999. 266 p.
- Bidaibekov E.S., Kornilov V.S., Kamalova G.B. Obuchenie budushhih uchitelej matematiki i informatiki obratnym zadacham dlja differencial’nyh uravnenij [The training of future teachers of mathematics and Informatics inverse problems for differential equations]. Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Serija «Informatika i informatizacija obrazovanija» [Bulletin of the Moscow city pedagogical university. “Informatics and Informatization of Education” series]. 2014. No. 3 (29). Pp. 57-69.
- Blehman I.M., Myshkis A.D., Panovko Ja.G. Prikladnaja matematika: predmet, logika, osobennosti podhodov [Applied mathematics: the subject of logic, especially the approaches]. M.: KomKniga, 2005. 376 p.
- Buhgejm A.L. Vvedenie v teoriju obratnyh zadach [Introduction to the theory of inverse problems]: monografiya. Novosibirsk: Nauka, Sibirskoe otdelenie, 1988. 181 p.
- Goncharsky A.V., Cherepashchuk A. M., Yagola A. G. CHislennye metody resheniya obratnyh zadach astrofiziki [Numerical methods for solving inverse problems of astrophysics]: monografiya. M.: Nauka, 1978. 335 p.
- Denisov A.M. Vvedenie v teoriyu obratnyh zadach [Introduction to the theory of inverse problems]: uchebnoe posobie. M.: Izd-vo Moskovskogo universiteta, 1994. 207 p.
- Kabanikhin S.I. Obratnye i nekorrektnye zadachi [Inverse and incorrect problems]: uchebnoe posobie. Novosibirsk: Siberian scientific publishing house, 2009. 458 p.
- Kornilov V.S. O mezhdisciplinarnom haraktere issledovanij prichinno-sledstvennyh obratnyh zadach [About cross-disciplinary character of researches of cause and effect inverse problems]. Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Serija «Informatika i informatizacija obrazovanija» [Bulletin of the Moscow city pedagogical university. “Informatics and Informatization of Education” series]. 2004. No. 1 (2). Pp. 80-83.
- Kornilov V.S. Nekotorye obratnye zadachi identifikacii parametrov matematicheskih modelej [Some inverse problem of identifying parameters of mathematical models]: uchebnoe posobie. M.: MGPU, 2005. 359 p.
- Kornilov V.S. Obuchenie obratnym zadacham dlya differencial’nyh uravnenij kak faktor gumanitarizacii matematicheskogo obrazovaniya [Training in inverse problems for differential equations as a factor of humanitarization of mathematical education]: monografiya. M.: MGPU, 2006. 320 p.
- Kornilov V.S. Gumanitarnye aspekty vuzovskoj sistemy prikladnoj matematicheskoj podgotovki [The humanitarian aspects of the university system of applied mathematical preparation of]. Nauka i shkola [Science and school]. 2007. No. 5. Pp. 23-28.
- Kornilov V.S. Gumanitarnyj analiz matematicheskih modelej obratnyh zadach [Humanitarian analysis of mathematical models of inverse problems]. Izvestiya Kurskogo gosudarstvennogo tekhnicheskogo universiteta [News of Kursk state technical university]. Kursk: KGTU, 2008. No. 3 (24). Pp. 60-65.
- Kornilov V.S. Psihologicheskie aspekty obucheniya obratnym zadacham dlya differencial’nyh uravnenij [Psychological aspects of teaching inverse problems for differential equations]. Nauka i shkola [Science and school]. 2008. No. 3. Pp. 45-46.
- Kornilov V.S. Laboratornye zanjatija kak forma organizacii obuchenija studentov fraktal’nym mnozhestvam [Laboratory sessions as a form of organization of teaching students fractal sets]. Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Serija «Informatika i informatizacija obrazovanija» [Bulletin of the Moscow city pedagogical university. “Informatics and Informatization of Education” series]. 2012. No. 1 (23). Pp. 60-63.
- Kornilov V.S. Obratnye zadachi v soderzhanii obucheniya prikladnoj matematike [Inverse problems in the content of teaching applied mathematics]. Vestnik Rossijskogo universiteta druzhby narodov. Serija «Informatizacija obrazovanija» [Bulletin of the Russian university of friendship of the people. “Education Informatization” series]. 2014. No. 2. Pp. 109-118.
- Kornilov V.S. Obuchenie studentov obratnym zadacham matematicheskoj fiziki kak factor formirovanija fundamental’nyh znanij po integral’nym uravnenijam [Training of students in the inverse problems of mathematical physics as factor of formation of fundamental knowledge of the integrated equations]. Bjulleten’ laboratorii matematicheskogo, estestvennonauchnogo obrazovanija i informatizacii. Recenziruemyj sbornik nauchnyh trudov [Bulletin of laboratory of mathematical, natural-science education and informatization. The reviewed collection of scientific work]. Samara: Samarskij filial MGPU, 2015. T. VI. Pp. 251-257.
- Kornilov V.S. Obuchenie studentov obratnym zadacham dlja differencial’nyh uravnenij kak factor formirovanija kompetentnosti v oblasti prikladnoj matematiki [Students learning the inverse problems for differential equations as a factor of formation of competence in the field of applied mathematics]. Vestnik Rossijskogo universiteta druzhby narodov. Serija «Informatizacija obrazovanija» [Bulletin of the Russian university of friendship of the people. “Education Informatization” series]. 2015. No. 1. Pp. 63-72.
- Kornilov V.S. Formirovanie fundamental’nyh znanij budushchih uchitelej informatiki i matematiki po funkcional’nomu analizu pri obuchenii obratnym zadacham matematicheskoj fiziki [the Formation of the fundamental knowledge of future teachers of Informatics and mathematics functional analysis when teaching inverse problems of mathematical physics]. Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Serija «Informatika i informatizacija obrazovanija» [Bulletin of the Moscow city pedagogical university. “Informatics and Informatization of Education” series]. 2015. No. 3 (33). Pp. 72-82.
- Kornilov V.S. Realizacija nauchno-obrazovatel’nogo potenciala obuchenija studentov vuzov obratnym zadacham dlja differencial’nyh uravnenij [Realization of scientific and educational potential of training of students of higher education institutions in the inverse problems for the differential equations]. Kazanskij pedagogicheskij zhurnal [Kazan pedagogical journal]. 2016. No. 6. Pp. 55- 59.
- Kornilov V.S. Bazovye ponyatiya informatiki v soderzhanii obucheniya obratnym zadacham dlya differencial’nyh uravnenij [The basic concepts of Informatics in the content of education inverse problems for differential equations]. Vestnik Rossijskogo universiteta druzhby narodov. Serija «Informatizacija obrazovanija» [Bulletin of the Russian university of friendship of the people. “Education Informatization” series]. 2016. No. 1. Pp. 70-84.
- Kornilov V.S. Teorija i metodika obuchenija obratnym zadacham dlja differencial’nyh uravnenij [Theory and technique of training to the inverse problems for differential equations]: monografija. M.: Izd-vo «OntoPrint», 2017. 500 p.
- Kornilov V.S. Formirovanie fundamental’nyh znanij po matematicheskomu modelirovaniyu pri obuchenii obratnym zadacham dlya differencial’nyh uravnenij [Formation of the fundamental knowledge on mathematical modeling in teaching inverse problems for differential equations]. Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Serija «Informatika i informatizacija obrazovanija» [Bulletin of the Moscow city pedagogical university. “Informatics and Informatization of Education” series]. 2017. No. 1 (39). Pp. 92-99.
- Kornilov V.S. Filosofskaya sostavlyayushchaya nauchno-obrazovatel’nogo potenciala obucheniya obratnym zadacham matematicheskoj fiziki [Philosophical component of scientific and educational potential of learning inverse problems of mathematical physics]. Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Serija «Informatika i informatizacija obrazovanija» [Bulletin of the Moscow city pedagogical university. “Informatics and Informatization of Education” series]. 2018. No. 1 (43). Pp. 59-65.
- Lavrentyev M.M., Romanov V.G., Shishatsky S.P. Nekorrektnye zadachi matematicheskoj fiziki i analiza [Ill-Posed problems of mathematical physics and analysis]: monograph. M.: Nauka, 1980. 286 p.
- Levchenko I.V., Kornilov V.S., Belikov V.V. Rol’ informatiki v podgotovke specialistov po prikladnoj matematike [The role of Informatics in the training of specialists in applied mathematics]. Vestnik Moskovskogo gorodskogo pedagogicheskogo universiteta. Serija «Informatika i informatizacija obrazovanija» [Bulletin of the Moscow city pedagogical university. “Informatics and Informatization of Education” series]. 2009. No. 2 (18). Pp. 108-112.
- Prilepko A.I. Izbrannye voprosy v obratnyh zadachah matematicheskoj fiziki [Selected questions in inverse problems of mathematical physics]. Uslovno-korrektnye zadachi matematicheskoj fiziki i analiza [Conditionally correct problems of mathematical physics and analysis]. Novosibirsk: Nauka, Sibirskoe otdelenie, 1992. Pp. 151-162.
- Romanov V.G. Nekotorye obratnye zadachi dlya uravnenij giperbolicheskogo tipa [Some inverse problems for equations of hyperbolic type]: monografiya. Novosibirsk: Nauka, 1972. 164 p.
- Romanov V.G. Obratnye zadachi dlya differencial’nyh uravnenij [Inverse problems for differential equations]: speckurs dlya studentov NGU. Novosibirsk: NGU, 1973. 252 p.
- Romanov V.G. Obratnye zadachi matematicheskoj fiziki [Inverse problems of mathematical physics]: monografija. M.: Nauka, 1984. 264 p.
- Samarskij A.A., Vabishevich P.N. Chislennye metody reshenija obratnyh zadach matematicheskoj fiziki [Numerical methods of the solution of the inverse problems of mathematical physics]: monografija. M.: Editorial URSS, 2004. 480 p.
- Timofeev Yu.M., Polyakov A.V. Matematicheskie aspekty resheniya obratnyh zadach atmosfernoj optiki [Mathematical aspects of solving inverse problems of atmospheric optics]: uchebnoe posobie. SPb.: Izd-vo Sankt-Peterburgskogo universiteta, 2001. 188 p.
- Yurko V.A. Vvedenie v teoriyu obratnyh spektral’nyh zadach [Introduction to the theory of inverse spectral problems]: textbook. M.: Fizmatlit, 2007. 384 p.
- Yakhno V.G. Obratnye zadachi dlya differencial’nyh uravnenij uprugosti [Inverse problems for differential equations of elasticity]: monografiya. Novosibirsk: Nauka, Sibirskoe otdelenie, 1990. 303 p.
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