The methodological office of the Department of Higher Mathematics is located in room 308. GAC. On the shelves of the room there is educational literature for 1st and 2nd year students, represented by methodical instructions for solving examples, methodical, educational and methodical and educational manuals written by the staff of the department for more than 25 years. Students can choose the necessary literature from almost all countries of the course “Higher Mathematics” to work on their topic of interest. In addition, the methodical office has various handouts for calculation and graphic tasks. Students can work with the selected methodological literature both in the office and take it with them on the security of a library card of the NTU “KPI” library.
O.P. Prishchenko, T.T. Chernogor
ORDINARY DIFFERENTIAL EQUATIONS
AND THEIR APPLICATIONS
IN SOLVING APPLIED PROBLEMS
Study guide for students of chemical specialties
The textbook aims to help students develop their mathematical thinking and acquire practical skills in solving differential equations. This textbook pays sufficient attention to a detailed explanation of the methods of solving typical equations of the theory of ordinary differential equations, its content fully corresponds to the program of the course of differential equations for students of chemical specialties.
The textbook contains brief theoretical information, detailed explanations of methods for solving typical differential equations, methods for solving applied problems with physicochemical content, 25 variants of calculation problems for them, and three independent works.
Reviewer: О. P. Nechuyviter, D. in Physics and Mathematics, Professor, Ukrainian Engineering and Pedagogical Academy of V. N. Karazin Kharkiv National University;
I. K. Kirichenko, Doctor of Physical and Mathematical Sciences, Professor, Kharkiv National Automobile and Highway University
T.V. Potanina
ORDINARY DIFFERENTIAL EQUATIONS
In this manual, the main types of differential equations, the solutions of which can be found analytically, are given, methods of their solution are indicated, and relevant examples are considered. The content of the manual is divided into practical exercises. Part of the examples is intended for solving during students’ classroom classes, the other part – for independent and homework. Options for independent and control work are given. Material on solving systems of differential equations and numerical methods for solving differential equations is presented in the appendices of the manual. For students of technical specialties.
Reviewers: V.M. Burlayenko, Candidate of Technical Sciences, Professor, National Technical University “Kharkiv Polytechnic Institute”;
I.V. Mykhaylenko, Ph.D. ped. of Sciences, associate professor, Kharkiv National Automobile and Road University
I.M. Katolyk
These guidelines include test tasks on the topic ‘Differentiation of a function of one variable’, which is one of the most important topics in the course of mathematical analysis and consists of sections ‘Differentiation technique’ and ‘Application of the derivative’. In order to successfully master this topic, students should be familiar with the concept of the derivative of a function, the table of derivatives and the rules of differentiation, the geometric content of the derivative and its application for analyzing the behavior of the function, constructing its graph, etc.
Reviewer Associate Professor I.V. Antonova
I.M. Katolyk, V.M. Oleksenko
In order to independently learn how to differentiate functions and systematize your mathematical knowledge, more than forty problems are solved in detail. It is desirable to know the proposed tables of derivatives and differentials of functions, which will significantly help in solving problems in higher mathematics both on the specified topic and in studying some other sections of higher mathematics in the future.
Reviewer Professor Yu.I. Pershyna
A.M. Haydash, T.A. Nemchenko
Methodical instructions for conducting a test control of knowledge in higher mathematics on the topic «Definite Integral» for students of all specialties of the National Institute of Energy, Electronics and Electromechanics, the National Institute of Mechanical Engineering and Transport, the National Institute of Chemical Technologies and Engineering.
Reviewer Professor Tuluchenko G.Ya.
G.Ya. Tuluchenko
This study guide is devoted to the organization of classroom and independent work of students in the process of studying the topic ‘Rows’. The content of the study guide is agreed with the work programs of the study discipline for students of all specialties
of the educational and scientific institute
of energy, electronics and electromechanics of NTU «KhPI». The purpose of the development of the study guide is to help in the effective organization of various types of educational activities of students, including remote and independent.
The training manual contains: theoretical material necessary for independent implementation
students of individual calculation tasks; examples of solving standard problems; variants of tasks for independent performance.
Yu.I. Pershyna, N.V. Cheremska, T.T. Chernogor
DERIVATIVE AND ITS APPLICATION
The educational and methodological manual for the higher mathematics course ‘Derivative and its application’ aims to help students in the formation of their mathematical thinking, as well as to acquire practical skills in differentiating functions of one variable and applying the derivative when studying a function and constructing its graph.
In this manual, sufficient attention is paid to the detailed explanation of the methods of solving typical problems on the topic «Derivative and its application». The context of the study material corresponds to the training program for students of technical specialties.
The educational and methodological manual consists of two parts, which include the necessary theoretical material, a detailed analysis of typical problems, examples for classroom and independent work, to which answers are added, and also contains 25 variants of calculation and graphic tasks for individual work of students.
N.O. Chikina, I.V. Antonova
FUNCTIONS OF SEVERAL VARIABLES. SCALAR FIELDS
The educational and methodological manual contains the main theoretical provisions, examples of problem solving and tasks for independent work of different levels of complexity from the sections of the higher mathematics course «Functions of several variables, Scalar fields». Intended for students and teachers of higher technical educational institutions.
The manual contains the theoretical part of the course and a sufficient number of solved practical problems, which have been taught to students by the Department of Higher Mathematics of NTU «KhPI» for several years. The content of the manual fully corresponds to the Work program of the educational discipline «Higher mathematics. Part 2». The authors have combined these two topics not by chance, because they consider it appropriate, since there is a direct connection between the practical application of these two topics. We are talking about the tasks of finding the smallest and largest value of functions in a closed domain and the well-known iterative algorithm – the gradient descent method.
Yu.I. Pershyna, O.P. Prishchenko, T.T. Chernogor
BOUNDARIES AND CONTINUITY OF FUNCTIONS
The educational and methodological manual is intended for students of technical specialties who study the topic «Boundaries and continuity of functions». Compiled on the basis of the authors’ experience of lecturing and conducting practical classes.
The work consists of eleven chapters. The first chapter provides brief information on the theory of boundaries. Chapters two through eight describe the technique of calculating limits and explain in detail the methods of solving typical problems, which are presented in the ninth chapter «Computational and graphical problems». In order to better navigate the material when completing tasks of the RGZ, next to each heading, the number of this task is indicated in brackets. The tenth section is the tests for operational control by teachers of students’ knowledge. RGZ and tests are developed for 30 variants. The eleventh chapter is reference material. At the end of the manual, answers to calculation and graphic problems are provided.
Yu.I. Pershyna, O.P. Prishchenko, N.V. Cheremska, T.T. Chernogor
The study guide is devoted to one of the most important topics of mathematical analysis – double and triple integrals. It consists of four parts. The first two parts cover the theoretical material on multiple integrals in detail. In the third and fourth parts of the manual, tasks related to the calculation of double and triple integrals are considered. The manual also contains tasks for independent work.
Yu.I. Pershyna, O.P. Prishchenko, N.V. Cheremska, T.T. Chernogor
INDEFINITE AND DEFINITE INTEGRALS
The educational and methodological manual consists of two parts «Indefinite Integral» and «Definite Integral», which include the necessary theoretical material, a detailed analysis of typical problems, as well as examples for classroom and independent work, to which answers are added, in addition, it contains tasks for control work.
O.P. Prishchenko, T.T. Chernogor
DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS
Teaching and methodical guide for the course of higher mathematics for students majoring in chemistry
The educational and methodological manual contains detailed explanations of methods for solving typical differential equations, methods for solving problems with a chemical content, and 25 variants of calculation problems for them.
DERIVATIVE AND ITS APPLICATION
Compilers: O.P. Prishchenko, O.S. Chorna
Methodical instructions for conducting practical classes
Methodical instructions for conducting practical classes on the topic «The derivative and its application» for students of all specialties. – Kharkiv: NTU «KhPI», 2018. – 36 p.
Compilers: N.V. Cheremska, T.T. Chernogor
Methodical recommendations for conducting practical classes
Methodical recommendations for conducting practical classes on the topic ‘Indefinite Integral’ consist of 6 practical classes and cover the higher mathematics course curriculum for students of all majors.
Compilers: I.I. Tsekhmistro, N.V. Cheremska, T.T. Chernogor
Methodical recommendations for conducting practical classes
The methodical recommendations contain problems on the topic ‘Definite integral and its application’ for five practical classes provided by the current working curriculum in higher mathematics for students of all majors.
from the course of higher mathematics
Compiler: T.V. Potanina
Tests from the course of higher mathematics were developed for their use in conducting operational control of the current and intermediate certification of students in order to assess the level of their preparation in this discipline.
T.S. Polyanska, O.S. Chorna
Educational and methodological manual for students of technical specialties of all forms of higher education institutions /span /p
span style=’font-size: 12pt’ The educational and methodical manual contains detailed methods of solving typical problems on the topic ‘Field theory’ and tasks for control work.
Compiler: T.S. Polyanska
Methodological instructions for conducting practical classes
Methodological instructions for conducting practical classes and tests in higher mathematics on the topic “Linear Algebra” for students of technical specialties of NTU «KhPI»