DIFFERENTIAL EQUATIONS AND MATHEMATICAL MODELS: AN EDUCATIONAL APPROACH
Main Article Content
Abstract
A documentary review was carried out on producing and publishing research papers on studying differential equations, mathematical models, and education. The bibliometric analysis proposed in this paper was to know the main characteristics of the volume of publications registered in the Scopus database during 2017-2021, identifying 90 publications. The information provided by the said platform was organized employing tables and figures categorizing the information by Year of Publication, Country of Origin, Area of Knowledge and Type of Publication. Once these characteristics were described, a qualitative analysis was used to refer to the position of different authors on the proposed topic. Among the main findings of this research, it is found that the United States, with 13 publications, was the country with the highest scientific production registered in the name of authors affiliated with institutions of that nation. The area of knowledge that made the greatest contribution to the construction of bibliographic material referring to the study of differential equations, mathematical models, and education was Mathematics, with 37 published documents, and the type of publication that was most used during the period mentioned above was the conference article, which represents 47% of the total scientific production.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
Duraj, S., Pepkolaj, L., & Hoxha, G. (2021). Adopting Drone Technology in Mathematical Education. HORA 2021 - 3rd International Congress on Human-Computer Interaction, Optimization and Robotic Applications, Proceedings11 June 2021 3rd International Congress on Human-Computer Interaction, Optimization and Robotic Applications, HORA 2021Ankara11 June 20.
Golinko, I., & Galytska, I. (2021). Mathematical modeling of dynamic heat-mass exchange processes for a spray-type humidifier doi:10.1007/978-3-030-55506-1_6 Retrieved from www.scopus.com
Gutiérrez, J. A., & Gallegos, R. R. (2019). Theoretical and methodological proposal on the development of critical thinking through mathematical modeling in the training of engineers. Paper presented at the ACM International Conference Proceeding Series, 941-948. doi:10.1145/3362789.3362828 Retrieved from www.scopus.com
Han, S., Lim, B., Lee, H., & Bae, S. H. (2018). Development of a user-friendly training software for pharmacokinetic concepts and models. Translational and Clinical Pharmacology, 26(4), 166-171. doi:10.12793/tcp.2018.26.4.166
Hu, F. (2021). Bidirectional promotion of ideological and political education in curriculum and online teaching-taking online teaching of mathematics as an example. Paper presented at the ACM International Conference Proceeding Series, 916-918. doi:10.1145/3456887.3457104 Retrieved from www.scopus.com
Jiménez, F. R. L., Ruge, I. A. R., & Jiménez, A. F. L. (2020). Modeling and control of a two wheeled auto-balancing robot: A didactic platform for control engineering education. Paper presented at the Proceedings of the LACCEI International Multi-Conference for Engineering, Education and Technology, doi:10.18687/LACCEI2020.1.1.556 Retrieved from www.scopus.com
Kassa, S. M., & Workineh, Y. H. (2018). Effect of negligence and length of time delay in spontaneous behavioural changes for the response to epidemics. Mathematical Methods in the Applied Sciences, 41(18), 8613-8635. doi:10.1002/mma.4926
Kawamura, M. L., Alleyne, A. G., & Sutanto, E. (2017). An educational laboratory experimental system for teaching chemical reaction process dynamics and control. Paper presented at the ASEE Annual Conference and Exposition, Conference Proceedings, , 2017-June Retrieved from www.scopus.com
Kaymakamzade, B., Şanlıdağ, T., Hınçal, E., Sayan, M., Sa’ad, F. T., & Baba, I. A. (2018). Role of awareness in controlling HIV/AIDS: A mathematical model. Quality and Quantity, 52, 625-637. doi:10.1007/s11135-017-0640-2
Kerr, R., Thomson, W. M., & Smith, D. J. (2019). Mathematical modelling of the vitamin C clock reaction. Royal Society Open Science, 6(4) doi:10.1098/rsos.181367
Khavinson, M. Y., & Kulakov, M. P. (2017). Gravitational model of population dynamics. Bulletin of the South Ural State University, Series: Mathematical Modelling, Programming and Computer Software, 10(3), 80-93. doi:10.14529/mmp170307
Kinoshita, F., & Takada, H. (2017). Numerical simulation of equilibrium systems while viewing stereoscopic video clips. Paper presented at the ICCSE 2017 - 12th International Conference on Computer Science and Education, 73-76. doi:10.1109/ICCSE.2017.8085466 Retrieved from www.scopus.com
Kouilily, F., Aboulkhouatem, F. Z., Yousfi, N., Achtaich, N., & El Khasmi, M. (2018). Modeling the social and epidemiological causes of hearing loss. Revista Mexicana De Ingenieria Biomedica, 39(3), 238-248. doi:10.17488/RMIB.39.3.3
Kráčalík, M. (2020). Mathematical modelling of continuum mechanics in context of industry 4.0 with emphasis on mathematical education. Paper presented at the 19th Conference on Applied Mathematics, APLIMAT 2020 Proceedings, 712-718. Retrieved from www.scopus.com
Kurniawan, F., Nugroho, S. M., & Hariadi, M. (2018). Smart city priority correlation using differential equation. Computing in Science and Engineering, doi:10.1109/MCSE.2018.2873936
Lambura, A. G., Mwanga, G. G., Luboobi, L., & Kuznetsov, D. (2020). Mathematical model for optimal control of soil-transmitted helminth infection. Computational and Mathematical Methods in Medicine, 2020 doi:10.1155/2020/6721919
Ledder, G. (2017). Scaling for dynamical systems in biology. Bulletin of Mathematical Biology, 79(11), 2747-2772. doi:10.1007/s11538-017-0339-5
Levy, B., Edholm, C., Gaoue, O., Kaondera-Shava, R., Kgosimore, M., Lenhart, S., . . . Nyabadza, F. (2017). Modeling the role of public health education in ebola virus disease outbreaks in sudan. Infectious Disease Modelling, 2(3), 323-340. doi:10.1016/j.idm.2017.06.004
Li, X., & Huang, Z. J. (2017). An inverted classroom approach to educate MATLAB in chemical process control. Education for Chemical Engineers, 19, 1-12. doi:10.1016/j.ece.2016.08.001
Liu, X. -., & He, D. -. (2020). Research on of competitive nonlinear dynamic information diffusion modeling in online social network. [在线社交网络的竞争性非线性动力学信息传播模型研究] Jisuanji Xuebao/Chinese Journal of Computers, 43(10), 1842-1861. doi:10.11897/SP.J.1016.2020.01842
Ma, W., Jin, M., Liu, Y., & Xu, X. (2019). Empirical analysis of fractional differential equations model for relationship between enterprise management and financial performance. Chaos, Solitons and Fractals, 125, 17-23. doi:10.1016/j.chaos.2019.05.009
Makarenko, O., & Samorodov, Y. (2021). To the statement of tasks of research of migration processes in education and science. Paper presented at the CEUR Workshop Proceedings, , 3126 222-227. Retrieved from www.scopus.com
Malakhov, A. A., & Fashchevskiy, N. N. (2019). MATLAB and SIMULINK educational potentiality in analysis of dynamic systems. Paper presented at the AIP Conference Proceedings, , 2195 doi:10.1063/1.5140169 Retrieved from www.scopus.com
Momoh, A. A., Abdullahi, H. M., Abimbola, N. G. A., & Michael, A. I. (2021). Modeling, optimal control of intervention strategies and cost effectiveness analysis for buruli ulcer model. Alexandria Engineering Journal, 60(2), 2245-2264. doi:10.1016/j.aej.2020.12.042
Mushanyu, J., & Nyabadza, F. (2018). A risk-structured model for understanding the spread of drug abuse. International Journal of Applied and Computational Mathematics, 4(2) doi:10.1007/s40819-018-0495-9
Narendranath, A. D. (2017). Introducing the galerkin method of weighted residuals into an undergraduate elective course in finite element methods. Paper presented at the ASEE Annual Conference and Exposition, Conference Proceedings, , 2017-June Retrieved from www.scopus.com
Nur, W., Trisilowati, Suryanto, A., & Kusumawinahyu, W. M. (2021). Mathematical model of schistosomiasis with health education and molluscicide intervention. Paper presented at the Journal of Physics: Conference Series, , 1821(1) doi:10.1088/1742-6596/1821/1/012033 Retrieved from www.scopus.com
Nyang’inja, R. A., Angwenyi, D. N., Musyoka, C. M., & Orwa, T. O. (2018). Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communities. Advances in Difference Equations, 2018(1) doi:10.1186/s13662-018-1875-5
Orfali, F., Vieira, F. P. B., & El Hage, F. S. (2018). A curricular innovation in the teaching of calculus in engineering programs. Paper presented at the International Symposium on Project Approaches in Engineering Education, , 8 232-239. Retrieved from www.scopus.com
Osman, S., Makinde, O. D., & Theuri, D. M. (2020). Mathematical modelling of listeriosis epidemics in animal and human population with optimal control. Tamkang Journal of Mathematics, 51(4), 261-287. doi:10.5556/J.TKJM.51.2020.2860
Ostadzad, M. H., Baroumand, S., & Mahmoudi, M. R. (2020). Optimization of public health education parameters for controlling the spread of HIV/AIDS infection. Symmetry, 12(4) doi:10.3390/SYM12040659
Ostadzad, M. H., Shahmorad, S., & Erjaee, G. H. (2020). Study of public health education effect on spread of HIV infection in a density-dependent transmission model. Differential Equations and Dynamical Systems, 28(1), 201-215. doi:10.1007/s12591-016-0310-1
Ponjavic, M. M., & Šekara, T. B. (2020). Singularity excitations and initial value problem in continuous LTI systems. IEEE Access, 8, 176750-176757. doi:10.1109/ACCESS.2020.3023334
Pratama, R. A., Ruslau, M. F. V., & Nurhayati. (2021). Global analysis of stage structure two predators two prey systems under harvesting effect for mature predators. Paper presented at the Journal of Physics: Conference Series, , 1899(1) doi:10.1088/1742-6596/1899/1/012099 Retrieved from www.scopus.com
Raczynski, S. (2018). Influence of the gregarious instinct and individuals’ behavior patterns on macro migrations: Simulation experiments. Journal of Human Behavior in the Social Environment, 28(2), 204-220. doi:10.1080/10911359.2017.1388758
Rhodes, A., & Hillen, T. (2019). A mathematical model for the immune-mediated theory of metastasis. Journal of Theoretical Biology, 482 doi:10.1016/j.jtbi.2019.109999
Rivera-Figueroa, A., & Lima-Zempoalteca, I. (2021). Motion of a simple pendulum: A digital technology approach. International Journal of Mathematical Education in Science and Technology, 52(4), 550-564. doi:10.1080/0020739X.2019.1692934
Rodriguez-Gallegos, R. (2019). Modeling complex problems in the teaching of mathematics. Paper presented at the Proceedings - IEEE 10th International Conference on Technology for Education, T4E 2019, 122-125. doi:10.1109/T4E.2019.00-38 Retrieved from www.scopus.com