Gerasimenko S.A., Pavlenko A.N.
ON THE PRESENTATION OF THE SECTION “ANALYTICAL GEOMETRY” IN ENGINEERING DIRECTIONS OF BACHELOR DEGREE COURSES IN FULL-TIME/CORRESPONDENCE FORMS OF STUDY ^{[№ 1 ' 2024]}
Currently, the main trends in higher education reform naturally lead to a significant reduction in the proportion of classroom lessons in the educational process, which has an extremely negative effect on the study of mathematical cycle disciplines due to their abstraction and often cumbersome presentation of the material. Thus, there is a need of increasing the effectiveness of contact work and strengthening the role of independent work of students. The above mentioned is also typical when studying the section “Analytical Geometry” in engineering bachelor courses, especially in full-time and correspondence studies. In order to increase the effectiveness of learning this section, a new applied approach to the study of analytical geometry in engineering bachelor courses in full-time and correspondence education is proposed, consisting in 1) consideration of the main tasks of analytical geometry based on natural science and technical specifications that arouse the interest of students and the relevance of which is beyond doubt, 2) the use of interdisciplinary connections with special disciplines, as well as with the history of natural science and technology, 3) moving the study of a significant part of the section “Analytical Geometry” to the independent work. To increase the effectiveness of the use of the considered approach, it is advisable to use relevant methodological support. As the latter, it is appropriate to use textbooks, collections of tasks and individual tasks, posters and 3d models, interactive guidelines integrated with applications written in high-level languages, generators of typical problems, etc.

Gerasimenko S.A., Pavlenko A.N.
ON UNIFICATION OF MULTIPLE, CURVILINEAR AND SURFACE INTEGRALS PRESENTATION IN ENGINEERING DIRECTIONS OF UNDERGRADUATE STUDIES ^{[№ 1 ' 2023]}
In modern world, the up-to-date trends in reforming of higher education lead to a significant reduction of classroom activities in the educational process, which extremely negatively affects the study of disciplines of the mathematical cycle due to their abstractness and often complexity of material presentation. Thus, there is a necessity to increase the efficiency of contact work and to widen the role of unsupervised work of students. This problem is especially evident in the study of the topic “Integral calculus for functions of several variables” in the engineering directions of undergraduate studies.
One of the factors that contribute to increasing the efficiency of contact and unsupervised work is the unification of the educational material presentation related to this topic.
In this article, we suggest a new approach to the study of multiple, curvilinear and surface integrals in the engineering directions of undergraduate studies, which include a unified parallel consideration of these integrals when using: 1) a preliminary revision of the topic “Defined integral” and the study of new material on this basis, 2) interdisciplinary connections, 3) information technologies.
It is advisable to use appropriate methodical support to improve the effectiveness of this approach. As the latter, it is appropriate to use tutorials, problem books and individual tasks, posters and 3d models, interactive guidelines integrated with applications, written in high-level languages, generators of typical tasks, etc.

Gerasimenko S.A., Pavlenko A.N.
DEDUCTIVE-EMPIRICAL APPROACH TO THE STUDY OF MATHEMATICAL CYCLE DISCIPLINES IN NATURAL SCIENCE COURSE IN MATHCAD ^{[№ 2 ' 2021]}
Nowadays, the main trends in the reform of higher education naturally lead to a significant decrease of classes in the educational process, which negatively affects the study of the disciplines of the mathematical cycle due to their abstraction and often complexity of material presentation. Thus, there is a need to increase the effectiveness of contact work and to strengthen the role of independent study of students.
One of the factors contributing to improving the effectiveness of contact work is the preliminary propedeutic independent study of the material when applying the empirical component of the deductive-empirical approach to teaching higher mathematics.
The proposed new deductive-empirical approach to the organization of non-auditory independent work in the study of the disciplines of the mathematical cycle by students of natural sciences should include the following directions/stages: 1) providing historical information on the empirical approach to solve mathematical problems arising in solving natural science and technical problems, 2) experiments leading to the expediency of introducing new concepts and experiments illustrating definitions, 3) empirical justification of difficult-to-prove and not obviously feasible theorems, 4) application of experimental method to find numerical values of quantities, 5) use of the experimental method to illustrate and check the results of solving a problem, 6) monitoring the effectiveness of applying a deductive-empirical approach to teaching mathematics.
To increase the efficiency of propedeutic independent study, it is necessary to use appropriate methodological support. And the last (depending on the section being studied), you can use interactive methodological guidelines integrated with applications written in various high-level languages, emulators of devices for conducting mathematical experiments, etc.
Thus, students of natural sciences should study mathematical disciplines in the inextricable unity of the traditional deductive presentation of educational material with an empirical approach to learning with the wide use of interactive technologies.

Gerasimenko S.A., Pavlenko A.N.
ORGANIZATION OF THE MATHEMATICAL CYCLE DISCIPLINES PROPAEDEUTIC STUDY OF NATURAL SCIENTIFIC AND ENGINEERING DIRECTIONS ^{[№ 2 ' 2020]}
Currently, the main trends in the reform of higher education naturally lead to a significant reduction of the part of classroom studies in the educational process, which is extremely negative for the study of the mathematical cycle disciplines due to their abstraction and often cumbersome presentation of the material. Thus, there is a need to increase the effectiveness of contact work and to strengthen the role of students’ independent work.
One of the factors contributing to an increase in the effectiveness of contact work is independent propaedeutic consideration of the material under study.
The approach to organizing extracurricular independent work in the propaedeutic study of the mathematical cycle disciplines by students of natural sciences and engineering should include the following steps: recalling the facts previously studied, presenting the natural science (engineering) applications in their historical retrospective and presenting the main ideas of this section. The latter is supposed to be performed the most clearly, with the maximum use of interdiscipline relations.
To increase the effectiveness of propaedeutic independent work, it is advisable to use appropriate methodological support. As the latter (depending on the section under study), you can use interactive study guide integrated with applications written in various high-level languages, presentations, educational films and study guide in written form.
Thus, the preliminary acquaintance with the new mathematical section should be during extracurricular independent work with the widespread use of interactive teaching technologies.

Gerasimenko S.A., Pavlenko A.N., Pikhtilkova O.A.
ABOUT SOME ASPECTS OF ORGANIZATION OF INDEPENDENT WORK ON THE DISCIPLINES OF THE MATHEMATICAL CYCLE STUDENTS OF NATURAL SCIENTIFIC DIRECTIONS ^{[№ 8 ' 2017]}
Currently, the main trends of reform of higher education naturally leads to a significant reduction in the proportion of classrooms in the educational process, and as a consequence, to a sharp increase of a role of independent work of students. Full improving the efficiency of the latter is a necessary condition for better learning of students of educational material. Approach to the organization of classroom independent work at studying of mathematical disciplines cycle students of science and engineering should include the following stages: a demonstration of practical application have been studied on the lecture method; independent decision students the same tasks, generated with the help of information technologies; automatic verification of the correctness of the decision of tasks and conclusions on the basis of the assimilation of educational material each student. To enhance effective learning of mathematics and to organize the operational control of independent work, it is advisable to use interactive guidelines, integrated with applications written in different high level languages. The contents of the online guidance: explanation of the basics of the method, giving concrete samples of application using multimedia technologies; generated with the help of information technology options of the model jobs; tasks of a creative nature with elements of research work. Thus, students receive the first skills of independent work should take place in the classroom under the guidance of a teacher, require reliable and timely monitoring of independent work, appropriate use of information technology to reduce the burden on the teacher.

Pavlenko F.N., Pikhtilkova O.A., Chetverikova A.G.
TO THE QUESTION ABOUT ORGANIZATION OF THE INTRODUCTION COURSE "MATHEMATICAL PROCESSING OF EXPERIMENTAL DATA" ^{[№ 7 ' 2015]}
The various approaches to introduction of the course "Mathematical Processing of Experimental Data" are considered in the article. It is noted that application of traditional statistical approach has a lot of essential shortcomings. The possibility of experimental finding of the necessary number of direct measurements of physical quantity sufficient for receiving the limit absolute error is proved. It is offered to imitate results of direct measurements by means of a computer mathematical MathCAD package, generating the random variable having normal distribution. As a result of numerous measurements there is not displaced estimation of an average square deviation providing a limit absolute error of result. Expediency of finding of absolute errors of results of indirect measurements by means of a method of borders for which it isn't required the knowledge which is far going beyond the school program is proved. Features of application of this approach to processing of results of indirect measurements are illustrated on two examples . Expediency of use of the interactive methodical instructions integrated with a computer mathematical MathCAD package for increase of efficiency of assimilation of this course by students of the natural-science and engineering directions is noted. In this case the operating control of correctness of mathematical processing of experimental data in audience leads to sharp increase in motivation of students to studying of the considered material.

Komakh Yu.A., Borzenok S.A., Kachegura L.V., Petrichuk S.V., Samokhina I.V., Volodin P.L., Pavlenko V.V., Polyanskaya E.G.
THE CLINICAL-IMMUNOLOGY STUDY OF INFLAMMATIVE-PROLIFERATIVE RESPONSES IN CHILDREN WITH CONGENITAL CATARACTS IN THE EARLY POSTOPERATIVE PERIOD (THE INTRODUCTORY RESULTS) ^{[№ 4 ' 2013]}
The results of the study of structure of early postoperative complications after congenital cataract aspiration with IOL implantation in children are presented in the article. At the moment of operation minimal age of the children was 2 years and maximum age was 14 years. The average age was 7,28±3,59 years. For 16 children (18 eyes) the comparison was made between the early postoperative period and the results of blood immunological tests. The risks factors of the early postoperative complications were researched.

Pavlenko A.N.
ABOUT SOLUTIONS OF OPERATOR EQUATION U=KW(U, λ) ^{[№ 4 ' 2010]}
In this article we prove existence no less two solutions of operator equation u=KW(u, λ), that is the generalization of the results got for operator equation u=λKW(u) and for its several individualizings.

^{[№ 12 (app.1) ' 2006]}

Panova I.E., Kazantseva E.E., Sherstneva Yu.V., Pavlenko E.S., Semenova L.E.
SURGICAL TREATMENT OF NODULAR FORM OF BASALT CELLULAR SKIN CANCER ^{[№ 13 ' 2004]}