Faniya Ahmetova

In this article, a version of the topic "Continuity of a function at a point" presentation is proposed. The necessary theoretical material is supported by examples. The tasks on this topic are selected in such a way that clearly illustrates the basic concepts of the topic. In addition, the selected tasks and examples represent methodological recommendations for homework doing and preparation for control work. The authors consider them as one of the students' education organizing forms and revealing residual knowledge on the topic. For convenience of the stated material perception, points of discontinuity classification is presented in the form of a table with illustration of typical examples. The content of the article will be useful for teachers and students.

In this paper, a technique is presented for applying MathCAD environment in the learning process by investigating some problems of functions behavior and graphs plotting. Specific features of the graph representation in MathCAD are given when there are points of function discontinuity. The tasks and examples being solved are methodical recommendations for doing homework. The authors consider them as one of the forms of students’ education organization and residual school mathematics knowledge revealing in first-year students. They give the methodical instructions on the applied programs package use for students teaching and show the prospects of their application, which increases the efficiency of the material perception. The simplicity of MathCAD interface made this system one of the most popular among mathematics support systems and, certainly, the most common among students. Active use of software will create the necessary professional competencies for students of technical specialties. The content of the article will be useful for teachers and students preparing for classes.

In order to increase the active use of application software packages for teaching students of technical and physical and mathematical specialties in higher education institutions, it is necessary to pay special attention to the use of software tools in solving various problems. In this regard, the paper discusses the teaching methods of integrating in MathCAD environment. Distinctive schemes and stages of finding indefinite and definite integrals are given. The problem of "non-convergent" integrals behavior in this computation environment is scrutinized here too. The author gives methodical recommendations on the software use in the educational process and shows the prospects of its application. All the actions performed during integration in MathCAD are analyzed on specific examples. Using application software package in teaching, will increase the learning process efficiency and help to develop necessary professional competencies for students. The contents of the article will be useful for teachers and students in preparing for practical classes.

The paper offers technique for presenting the topic " Linear combinations functions curves containing a modulus sign ". The article contains brief presentation of theoretical information in the field of functional dependence of elementary functions. The functions curves presented in the form of linear functions moduli sum or difference are analyzed in detail. The authors demonstrate practical methods that allow you to plot sketches of functions curves with different complexity levels. They give examples of typical tasks necessary for skills improving. The purpose of this work is to provide a systematic description of methods for functions with modulus curves plotting. At the same time, the main attention is paid to the methods of plotting, and not to the study of certain functions types.

The article contains a brief presentation of theoretical information in the field of functional dependence of elementary functions. Practical methods that allow you to draw sketches of functions’ curves of different complexity levels are demonstrated here. In particular, the plotting of functions’curves containing modulus usually causes considerable difficulties for university entrants and first-year students. The purpose of this work is to give algorithm for plotting curves of functions containing moduli to which linear transformations are applied. The main attention is paid to the methods of plotting, and not to the study of certain types of functions.