Olga Vergazova

In order to improve the level of mathematical training of engineering majors, it is necessary to pay special attention to those mathematical issues, without solid knowledge of which successful learning in a university is impossible. This article demonstrates methods of organizing classroom or independent students’ work by the example of solving tasks on the topic “Research of numerical series for convergence”. The article may be interesting to teachers as well as Mathematics and Engineering majors.

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.

The limit of function and continuity of function concepts are among the most difficult-to-digest concepts of school mathematics, and often cause difficulties for students. This work suggests a methodology for the presentation of the topic "The function continuity concept " in the courses of algebra and analysis in high school and mathematical analysis course for University first-year students. The aim of this work is to substantiate this concept with examples from physics, to provide deep understanding of continuity concept by high school and University students, to figure out the physical and geometric meaning of this concept. The work summarizes basic theoretical knowledge, typical examples and tasks for proof. The article is based on the experience of teaching mathematical analysis in technical university and it will be useful both for teachers in conducting practical classes and for students in their independent work on the topic.

With the aim of mathematical training level raising among future students of mathematical and technical professions, we need to pay special attention to those math questions without solid knowledge of which successful learning in a University is impossible. In this article, on examples of solving tasks on the topic "Logarithmic inequalities", the author shows the possibility of differentiated approach to the training of future students of technical or mathematical higher schools who will have to learn a course of higher mathematics, particularly mathematical analysis. The development of skills using the traditional method based on the monotonicity of the logarithmic function, and a rationalization method to solving logarithmic inequalities is an important part of high school students training for passing the Unified State Examination in mathematics on advanced level. The content of the article may be interesting to teachers and students who want to enter Universities to study technical or mathematical areas.

This work suggests a methodology for the presentation of the topic "Solution of plane figures areas calculating problems " in the course "Integral calculus". The article is based on experience of mathematical analysis teaching in technical university and it will be useful both to teachers in conducting practical classes and to students in their independent work on the topic. The aim of this work is to help students to acquire and develop skills of integration methods application for various problems solving. When solving tasks on the areas calculation students have as a rule difficulties working with polar coordinates and functions defined parametrically. In this case, it is useful to consider the problem solution in different ways. The basic theoretical information is briefly stated in this article. The author gives examples and standard tasks that are necessary to improve integrating skills and provides information from the history of mathematics which helps to develop cognitive interest to the explored subject.