One of the most important disciplines for the training of civil engineers is engineering and computer graphics. However, traditional training in engineering graphics does not bring tangible results, so there is a need for the introduction of modern innovative approaches and methods. It is proposed and justified the use of a combined approach to teaching engineering graphics, based on the combination of three-dimensional modeling in AutoCAD 2018 and traditional, on paper, manually. Studies conducted on the basis of the Kazan State University of Architecture and Civil Engineering have shown the feasibility of using a combined approach. So, as a result of the experiment, it turned out that the most effective assimilation of educational material according to the results of graphic work was demonstrated by the group of students who, when it was used, used both the capabilities of 3D modeling and the ability to manually perform graphic work, with this approach, students receive additional skills, which will become relevant in their future professional activities.
The goal of this study is to develop and apply an approximate method for calculating integrals that are part of models using Riemann-Liouville integrals, and to create a software product that allows such calculations for given functions. The main results of the study consist in the construction of a quadrature formula for an integral, and the cases where the density of the integral is a function from the spaces of continuous functions with generalized derivatives with weight and the Helder classes of functions with weight were considered. For the proposed quadrature formula we further investigated the error of its approximation in the spaces of continuous functions and quadratic-summing functions with weight. As a result of the study, effective error estimates of the approximating apparatus in the proposed classes of functions have been established. In addition, the approximated method has been implemented on the computer in the form of a program in the C language. The significance of the obtained results for the construction industry consists in the fact that when solving problems, including problems on finding the shapes of structures, taking into account the properties of materials, environmental changes, in the models of which the Riemann-Liouville integrals are used, it will be possible to apply an approximate approach, the quadrature formula proposed in the article.
Formation of students' research competencies is an urgent and important task of universities, which fits into the implementation of the strategy of scientific and technological development of the Russian Federation. The paper discusses the impact of project-based learning technology of mathematics on the formation of research competencies of students-architects. The distinctive features of this work are: the use of design technology of teaching mathematics on the basis of an educational architectural project; identifying the criteria and indicators for the level of research competence of architecture students The paper presents the results of experiments confirming the effectiveness of the proposed technology. The perspectives of using project technology in architects' training are discussed.
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