Modeling of various phenomena in engineering work is always a kind of simplification of real processes, aiming at a model where a certain level of mathematical theory and computational procedures is sufficient. If the complexity of the required theory corresponds to the general mathematical competence of engineers, then technical problems can be treated separately in engineering (or physical) models without regard to the mathematical background. However, in some advanced engineering fields, the harmonized development of engineering and mathematical models and toolboxes is necessary to find efficient solutions. For example, modeling variable structure systems in ideal sliding mode requires a mathematical toolbox that goes far beyond general engineering competence through the theory of discontinuous right-hand-side differential equations. Although sliding mode control is popular in practice and the concept of sliding mode allows a significant reduction of model complexity, its exact mathematical description is rarely encountered. The problem of friction compensation of a micro-telemanipulator using sliding mode control demonstrates a harmonized application of the mathematical and engineering approaches. Based on Filippov’s theory, the ideal sliding mode can be discussed. Although an ideal system cannot be implemented in reality, the real systems can be kept close enough to it; therefore, the discussion of the solution of the ideal model is important for practical applications. Although several elements of the topic are available in the literature, in this paper a unique complex approach is given for users of sliding mode control with experimental considerations, different engineering models, and codes. The paper concludes that sliding mode control is a case where engineering and mathematical modeling are inseparable and requires the competence of both fields.

To apply mathematical methods to physical or other real life problem, we have to formulate the problem in mathematical terms. It means that, we have to construct the mathematical model for the problem. Many physical problems shows the relationships between changing quantities. The rates of change are represented mathematically by derivatives. In this case the mathematical models involve equations relating an unknown function and one or more of its derivatives. These equations are the differential equations. In this article, teaching the analysis of Newton's cooling model to engineering students is presented as one of the applications of separable differential equations. To apply mathematical methods to physical or other real life problem, we have to formulate the problem in mathematical terms. It means that, we have to construct the mathematical model for the problem. Many physical problems shows the relationships between changing quantities. The rates of change are represented mathematically by derivatives. In this case the mathematical models involve equations relating an unknown function and one or more of its derivatives. These equations are the differential equations. In this article, teaching the analysis of Newton's cooling model to engineering students is presented as one of the applications of separable differential equations.

The height determination of control and detail points is essential during the process of planning and manufacturing in the practice of civil engineering. Planning maps are drawn for the former, while the intended plan is set out on the ground during manufacturing, and after the manufacturing the completed installation is mapped. Using the same reference system in all three steps, both horizontally and vertically, is recommended even though in some cases it is unavoidable to change from one reference level to another. Regardless of the fact that both refer to the mean sea level of the Baltic Sea, this can create difficulties, since the difference between the EOMA and Bendefy networks used in Hungary shows varying values depending on the geographical location. The aim of the analysis is to determine a constant difference regarding the analysed settlements based on the common points of the networks.

This paper presents two complementary classes of analytical benchmark problems for the one-dimensional wave equation governing longitudinal vibration of a prismatic rod with mixed (clamped–free) boundary conditions. The first benchmark class consists of classical initial-value problems and includes both compatible and incompatible initial data at the space–time corners, highlighting their influence on convergence, regularity, and termwise differentiation of displacement, velocity, and axial force series representations. The second benchmark class prescribes the displacement at two time instants (initial and final time), leading to a fundamentally different modal structure and revealing spectral conditioning effects governed by the ratio $L/\left(c{t}_e\right)$. The derived closed-form solutions provide reference configurations for verification of transient numerical solvers, particularly in scenarios where classical smooth compatibility assumptions are not satisfied.

Jelen dolgozat a PADME (Pallas Athéné Domus Meriti) Alapítvány támogatásával valósult meg. Az elektronikus oktatásnak számos előnye és hátránya van. Ezek közül szeretnék rávilágítani néhány fontosabbra, valamint ismertetni azon felméréseim eredményeimet, amelyeken az egyetemi hallgatók modellalkotási, absztrakciós és lexikális tudását mértem fel az online oktatás előtt és után.

On February 11, 2021, I gave a motivational lecture at the Tamás Esze High School in Mátészalka, and I completed a series of test tasks with the students. In this article, I looked for an answer to how students who are about to graduate approach to solving math problems. The main objective was to investigate whether they prefer to solve purely mathematical or application-oriented tasks, and in which one they achieve better results. In this paper, I analyze the results obtained.