Keyword: «numerical methods»

In the process of studying and in the content of such an academic discipline as “Numerical Methods”, many components of the future engineer training process are reflected: the applied trend of mathematics, the necessary conditions for the formation and further development of methodological knowledge and skills, the opportunity to establish associations between various university disciplines. In addition, in this case, it is also possible to implement a differentiated approach to learning during the classroom and independent work of the student. The content of the article may be interesting for teachers, as well as for students of technical or mathematical specialties.

This paper discusses the organization of students' project work on the example of the discipline numerical methods. Effective approaches to using the possibilities of numerical methods in the organization of design work are given. In particular, to solve complex problems using numerical methods, students are required to have deep mathematical knowledge, skills in the field of information technology, as well as a good command of a programming language. Design work is shown on examples of numerical methods for solving nonlinear equations, numerical integration problems. The Qt Designer program for working with a graphical interface in the python language is also considered.

The method of numerical simulation of diffraction processes in a symbolic and numeric computing environment Maple is considered.

This article examines the synergy of computer science and mathematics through the prism of an interdisciplinary approach to studying Cauchy sequences and describes how the interaction of mathematical theories and algorithmic practices allows us to create more efficient and robust algorithms for solving complex problems. The article analyzes the use of Cauchy sequences in various areas of computer science, such as numerical computing, data processing and machine learning, and emphasizes the importance of a mathematical foundation for the development of algorithmic thinking. Conversely, examples of the practical application of an interdisciplinary approach are analyzed, demonstrating how the synergy of the two sciences can lead to new discoveries and innovations. But this is possible only if there is a developed skill of independent problem solving, using a variety of tools. Thus, the article talks not so much about an interdisciplinary approach, but about the formation of universal literacy of students through the synthesis of mathematics and computer science. This article explores the interaction between the mathematical concept of the Cauchy sequence and its application in computer science, especially in the context of algorithmic thinking. At the same time, both mathematics and computer science are considered in the dominant format, that is, the role of each of the subjects is not reduced to the level of a tool. That is, on the one hand, the article reveals mathematical principles that help to form clear and effective algorithmic solutions in programming and data analysis. On the other hand, machine learning and optimization algorithms help to improve mathematical calculations in data processing. Thus, the article includes examples of the application of Cauchy sequences in various areas of computer science, such as numerical methods, machine learning and data processing. The main approaches to teaching algorithmic thinking are also discussed, with an emphasis on the importance of a mathematical foundation. This article presents the mutual penetration of two disciplines, with an attempt to maintain a balance between them, without translating into a tool format.

The relevance of this research topic stems from the fact that students in engineering fields, in addition to knowledge of the mathematical methods of computational mathematics, must understand their applied significance and be able to develop software to solve applied problems, implementing the methods studied in the form of computer programs. Currently, there is a transition from software provided to educational institutions by foreign companies to domestic products, which requires training preservice engineering students with the use of domestic software. The aim of this article is to describe the authors' original approach to organizing a laboratory practical course on numerical methods. This approach allows students to more deeply understand the essence of methods, realize their interrelationships, and master the elements of functional-object programming as well as the Algozit software environment. The research methods used include numerical methods for solving basic mathematical problems in algebra, analysis, and other fields, as well as functional-object programming. The result is an approach developed by the authors for organizing laboratory work on numerical methods for students majoring in engineering. This approach is based on the development of an innovative programming paradigm and the domestic software product for engineering calculations, the Algozit Functional-Object Programming Environment. This approach includes studying the analytical foundations of numerical methods and retention of this knowledge by solving simple tasks without developing computer programs, as well as developing programs in the Algozit environment for a more in-depth study of the methods and their application to solving applied problems. The theoretical significance of this work lies in the generalization and systematization of materials for laboratory practical training using the developed approach. The practical significance lies in the fact that the presented approach can be used in laboratory practical training in the disciplines "Numerical Methods" and "Computational Mathematics" for students majoring in engineering.