Mathematics and Physics

В учебном пособии рассмотрены вопросы применения дифференциальных уравнений математической физики для моделированиятехнических систем, и методы их точного и приближенного решения. Предложены примеры решения и варианты типових задач для расчетной работы и проведения практических занятий. Для студентов, обучающихся понаправлениям: «Прикладная механика», «Инженерная механика», другим направлениям подготовки бакалавров и магистров высших учебных заведений.
Ссылки для цитирования:
1. Усов А.В., Шпинковский А.А., Шпинковская М.И.
Уравнения математической физики в моделировании технических систем: Уч. пособ. для студентов высших учеб. заведений. – Киев: Освіта України. 2014. – 190 с.
2. Usov A.V., Shpinkovski A.A., Shpinkovska M.I. (2014). Uravnenija matematicheskoj fiziki v modelirovanii tehnicheskih sistem [Equations of mathematical physics in the modeling of technical systems].  Kiev: Osvіta Ukraїni [in Russian].

In Chilean universities, a large proportion of engineering students abandon their studies within the first year. There is a variety of reasons for this phenomenon. It is also a fact that a high number of students fail their first year physics and/or math courses. We believe that the high dropout rate is related to failing physics and math courses (sometimes more than once); however, that relation has not been studied in Chile. In general, there is a consensus in the literature that these two phenomena (failing a course and dropping out) are caused in some degree by the limited preparation on these sciences that students receive in precollege education, as well as by the traditional teaching strategies (lecturing being a quite common teaching strategy in physics and math courses). However, this study takes a different approach. We believe that another strong reason for failing courses and dropping out of school might be related to students’ perception of the relevance of physics and mathematics to their professional career, which is, in this case, engineering. In this study 232 students taking first and second year physics and math courses at a large private university in Chile participated. We used a Likert-scale instrument in which students chose from a “Totally agree” to “Totally disagree” scale of statements related to relevance of science and mathematics for future career and study. The results of this study discuss four aspects: 1) the students’ perceptions of the relevance of physics and mathematics of scholar engineering and professional engineering practices, 2) the comparison of students’ perceptions of the relevance of physics to that of mathematics, 3) gender differences on those perceptions and 4) the relation of those perceptions to their performance in the course. As conclusions, we present the consequences for that practice and some recommendations for instructors and course designers.

There is a connection between string theory and the Riemann's zeta function: this is an interesting way, because the zeta is related to prime numbers and we have seen on many occasions how nature likes to express himself through perfect laws or mathematical models. In [6] the authors showed all the mathematical and theoretical aspects related to the Riemann's zeta, while in [9] showed the links of certain formulas of number theory with the golden section and other areas such as string theory. The authors have proposed a solution of the Riemann hypothesis (RH) and the conjecture on the multiplicity of nontrivial zeros, showing that they are simple zeros [7][8]. Not least the situation that certain stable energy levels of atoms could be associated with non-trivial zeros of the Riemann's zeta. In [6] for example has been shown the binding of the Riemann zeta and its non-trivial zeros with quantum physics through the Law of Montgomery-Odlyzko.

This study focuses on bridging the gap between physics and mathematics by teaching an integrated first-year college course of physics and mathematics using Modeling Instruction (MI) and models and modeling perspective. This innovation involves redesigning the course’s content, combining teaching strategies, reshaping the classroom setting, and using technology. In this study 37 first-year engineering students were enrolled in the integrated course. The research questions were: What elements of the physical and mathematical models do students use when solving a complex real problem? How does the consistency of students’ model lead to a robust understanding of the problem? To answer these questions, students worked collaboratively on a project that involved the analysis of an extreme bungee jump. The performance of the students in this project revealed: a) students’ integration of physical and mathematical models, b) different representations used in the solution and c) robustness of students’ models.
As conclusions we can state that as the students constructed more robust models, these were more helpful in their problem solving. Participating students constructed physical models that led them to mathematical models that required numerical methods. The use of numerical methods with technology as an aid in solving complex problems is part of the natural integration of physics, math and technology. Final presentations in a poster fair format provided students with the space and environment to present and share the models they constructed. Students were required to show their work and process to arrive to such solution to their peers. More importantly, the final project offered students the opportunity to realize how empowered they were in solving complex and non-familiar problems.