Abstract:

The development of information and communication technologies in terms of software leads to the improvement of existing software products and the emergence of new software products. Teachers do not always use the best software products in the process of teaching students. For teachers of mathematics at a technical university, graphic systems are of great interest, these systems are currently rapidly improving and expanding the set of their properties and functions.

Visualization of mathematical objects on a plane and in three-dimensional space is of great importance during studying of higher mathematics by construction students. Therefore, mathematics tutors are interested in using 3-D plotters, and also interested in choosing the best of these software products. This study provides an overview of modern tools for constructing surfaces in three-dimensional space. We considered the application of graphic systems to the visualization of the basic concepts of a function of two variables and selected the most appropriate graphic systems for our tasks. We also identified those tasks of the section of the function of two variables that allow good visualization. These are tasks related to the construction of a surface, level lines, a tangent plane and a normal, a gradient and a directional derivative, the study of a function for an extremum. We have developed examples, their solution allows good visualization, we used the equations of second-order surfaces for this. We obtained the examples’ analytical solution and showed the interpretation of our solution on a 3-D image created using a graphic system. Using the obtained graphic images when discussing mathematical problems with first-year students, we mentioned their increased interest in the fact that abstract mathematical equations can be seen in space, rotated, and viewed from different angles. We managed to prove that students can be taught to accompany their solutions to problems on the topic of functions of two variables with 3-D images and this will increase their interest in the studying subject.

Acknowledgement:
The research was carried out with the financial support of the Kuban Science Foundation in the framework of the scientific project № FSR-HS-20.1/37.

Keywords:

Educational resources, information and communication technologies, 3D images, graphic images, visualization, plotter, three-dimensional space.