Integrated educational handbook as a means of training mathematics of technical students based on integrative and activity based approaches
In this article we consider the method of using an integrated textbook on vector algebra for students of a technical university on the basis of integrating mathematics and other other disciplines in the system of higher engineering education on the basis of the activity approach. The manual will be useful for teachers and math classes, as a demonstration of the application of vector algebra in physics, and in physics - to demonstrate the application of physics in mathematics, as well as to students who have attended a course in higher mathematics and started studying physics, to repeat an important section for them. The issue of the development of teaching aids in higher mathematics in which the integration of mathematics with other disciplines in the system of higher professional education is carried out is very urgent and requires a theoretical and methodological justification. In modern didactics there is no unambiguous understanding on what grounds the model of an integrated teaching aid should be built. However, the most productive is the understanding, under the integrated textbook on mathematics for students of a technical university, a training manual that implements an integrative approach to learning, based on the principles of scientific, integrity, continuity, objectivity, individualization and differentiation of learning, and the activity approach in accordance with the principles of primary activity, professional orientation, activity goal setting, activity definition of the content of training. The main feature of such a manual is the possibility of its use in teaching both mathematics and other disciplines, in which a mathematical apparatus is used to solve problems. This summary is widely used in teaching not only higher mathematics, but also other disciplines, such as physics, theoretical mechanics, theoretical fundamentals of electrical engineering, hydrodynamics, the theory of mechanisms and machines, the resistance of materials. When teaching mathematics, a textbook can be used in a basic summary for the organization of educational activities in lectures. In practical exercises, the semantic abstractmanual can be used at various stages of the activity to update knowledge, consolidate knowledge, form skills, and control the formation of skills and habits.