Pospelkina D.D., Chernitskaya O.V., Atanova M.Yu.

*Oles Honchar Dnipropetrovsk National University, Ukraine*

**THE DEVELOPMENT OF E-LEARNING COURSE «CALCULUS OF VARIATIONS. BASIS OF APPROXIMATION THEORY»**

Nowadays the development of information technology enables each student who has an access to a computer to study material independently in an appropriate time and in individual rate. Such possibility increases the effectiveness of the educational process greatly. It is convenient for people who have free access to a computer and do not have enough time or physical possibilities for visiting lectures. These facts determine the relevance of the represented work.

Let's consider the e-learning course «Calculus of Variations. Basis of Approximation Theory» in details.

The developed electronic training course includes the following main parts:

· theoretical material for independent review of the subject;

· self-test questions after each topic;

· test system with automatically processing and evaluation of results;

· laboratory works;

· examples of common solving of tasks;

· interesting historical material.

Also, the e-learning course includes a list of useful literature. This information will help those who wish to deepen their knowledge on the subject.

All theoretical material is presented in the form of lecture notes and has a comfortable clear structure for maximum efficiency of perception in the course. The tests were equipped with a timer that provides a limited time on task. Also this part of course was complicated by the random output on the screen, which increases the adequacy of the results.

The main advantage of the presented e-learning course is the ability to edit and update all material presented in course. Such procedure does not expect from the teacher special knowledge of programming language. He has to know only the basics of using the computer. So the editing process does not require the participation of the developer.

Also e-learning courses include such possibilities as studying represented material any time at home. However, this excludes the possibility of direct communication with the teacher during the learning process. The solution of this problem is the connection of e-learning course to the Internet. Therefore special elements of software were developed in the represented course too. These elements enable users to communicate with the teacher via the Internet. Student is able to send an e-mail with completed tasks for checking, questions and comments from the course. Also he can review the following teacher's answers and give some comments. It does not require additional connection to the mailbox or special starting of web browser. Such software also provides the opportunity for direct connection to the Internet. It means the transition from a fixed located on your computer e-learning course to its web elements in the Internet. This makes the course more mobile and accessible and more convenient.

The main result of the development of the e-learning course is the results of users work with the program. Such result is the results table, which shows the success of student's study. The teacher presents the assessment according to this table or students evaluate their progress and knowledge themselves.

Also conclusions about the efficiency of the course can be based on the represented information. Because the appointment of the results table is not only to output information about individual student progress. This table helps to control the content of training course material and correct all defects which were found. The level of difficulty of each test should be in line with the level of knowledge that every student can get in the particular part of the course. For example, a hundred of people were tested in some part of course. Their results were inserted into the table of results. If ten of these students have a minimum number of points and the other ninety students have good and excellent grades, then it says that those ten people understand the learning material poorly. But there can be the other situation. Ninety people had good and excellent results in all sections except this one. And their number of points decreased in this specific part of course. This discrepancy shows that the contained material incomprehensibly represented in the considered section or is not matched with tests for this chapter. That is the way for detecting the main points of incompletely developed stage of testing the software.

Thus, the table of tests results of e-learning course «Calculus of Variations. Basis of Approximation Theory» is an indicator of its quality, information content, clarity and convenience for the student. Because if the student learns the material successfully and has been successfully tested as the result, then it means that all elements of the course harmoniously interact with the object of study, and became effective means of distance learning or independent study students of mathematical subject. So, the teacher is able to evaluate working capacity of the course. He can decide whether it is appropriate to introduce it in the learning process, based on a sample of students.

Presented course can be used not only for individual students but also for use by teachers in the classroom. Teachers can automatically check students' knowledge and share parts of lectures with the help of this course.

Thus, prepared e-learning course has the following advantages:

· facilitates understanding of the material under study;

· allows adaptation to the needs of the student, his level of preparation, speed of learning, intellectual ability;

· provides the ability to edit and update all material presented in course without developer help;

So it can be concluded that e-learning courses are the perspective direction of informatization of education which has a great potential. Their importance will only increase.

**Literature:**

1. Поспєлкіна Д.Д. Розробка програмного забезпечення електронного навчального курсу «Варіаційне числення. Основи теорії апроксимації» / Д.Д. Поспєлкіна // Конференція за підсумками науково-дослідницької роботи ДНУ ім. О.Гончара «Проблеми прикладної математики та комп’ютерних наук». – Д.: ДНУ, 2011. – 33 с.