This page contains information about some textbooks developed by our staff members. You can view the textbooks (including Russian and Ukrainian ones) on this page.

▲ Higher Mathematics. Problem-solving and variants of typical calculations (Edited by Prof. Kurpa L.V.)

   The textbook “Higher Mathematics” in four volumes is based on materials that were published earlier in books “Вища математика” and “Higher Mathematics” under the editorship of Prof. Kurpa L.V. presented in 2 volumes in 2002 and 2004. However, this edition is fundamentally overworked, extended, supplemented, and given in 2 languages (Russian and English). For each theme, only the main theoretical knowledge is expounded in an organic form. Special consideration is given to methods of problem-solving. It helps the student to understand theoretical materials more profoundly and teaches him to apply mathematical tools to solve concrete tasks. Individual tasks (30 variants) and also test questions and control tasks are presented to each theme. By means of these tasks, the student can check their preparedness to self-dependent carrying out individual tasks. Both test tasks and individual tasks are supplied with answers that will help the student to check the accuracy of the obtained solution. The given textbook is characterized by examples of tasks solved in Maple software, in which text of programs is also presented. Taking into account modern requirements to engineering professional skills and the high level of information technology development, the authors have decided to include in the textbook primary information about one of the modern mathematical systems “Maple”. The authors think that the parallel solution of many problems of higher mathematics by means of the package Maple and without them allows checking the solution obtained by students independently. Using these packages will set free an engineer of routine mathematical calculations and transformations in the future. It will promote the intensification and development of the creative approach to executing either problem. Therefore, the textbook contains tasks solved by means of the system “Maple” together with worked-out programs. This textbook will be very useful not only for students from UIC but also for foreign students learning in Ukraine. The authors are very grateful to many teachers that gave answers to individual tasks including E.S. Arkhipova, L.V. Bolotina, T.L. Kornil, L.P. Lemesheva, N.N. Yasnitskaya, and others.

 

▲ Higher Mathematics Problem-solving and variants of typical calculations. (Edited by Prof. Kurpa L.V.)

The educational textbook includes theoretical material of main sections of higher mathematics: linear algebra, analytical geometry and calculus, fundamentals of differential calculus of function of several variables, multiple, curvilinear and surface integrals, field theory and sets, examples of solving typical problems and variants of typical calculations.

  

 

▲ Elements of Linear Algebra and Analytic Geometry  / Rudneva G.V. Elements of linear algebra and analytic geometry : The textbook. – Kahrkiv: НNTU «KhPI», 2008. – 168 p.

Author: G.V. Rudnyeva

 

The textbook “Elements of Linear Algebra and Analytic Geometry” presents a course of mathematics suitable for undergraduate students of technical universities and has grown out of a course of lectures given by the author at National Technical University “Kharkiv Polytechnic Institute” during the past four years to the students studying the mathematical courses in English.

 

 

 

 

▲ Differential Calculus for One Variable Functions / Kurpa L.V., Shmatko Т.V.  Differential calculus for one variable functions : The textbook for the students of technical universities. – Kharkiv: NTU KhPI, 2008. – 160 p.

Authors: L.V. Kurpa, T.V. Shmatko

 

 

 

 

 

 

 

 

 

▲  Differential and Integral Calculus for One Variable Functions. / L.V. Kurpa, T.V.Shmatko. Differential and integral calculus for one variable functions: The textbook. – Kharkiv: NTU KhPI:  2017. – 324 pages.

Authors: Kurpa L.V,  Shmatko T.V.

This handbook includes theoretical material with all the necessary proof of the theorems for a section of Higher Maths “Differential and integral calculus for functions with one variable” Proposed materials correspond to education programs from higher mathematics for technical universities related to the point section. The handbook does not purport to address the presentation of the complete course of higher mathematics, but to some extent compensates for the lack of English literature in the course of higher mathematics in Ukraine.

The authors hope that the manual will help students in learning this section of Mathematics and will be useful for teachers who give lectures in English.

 

 

 

 

▲ Differential and Integral Calculus for Functions with Several Variables / L.V. Kurpa, T.V. Shmatko. Differential and integral calculus for functions with several variables. – Kharkiv : NTU “KhPI”, 2012 – 252 p.

Authors: L.V. Kurpa, T.V. Shmatko

Theoretical material of differential calculus of several variables, multiple and curvilinear integrals is proposed The educational textbook includes problems that are recommended to solve as classwork and as homework. Variants of individual tests are created for each subject. For students and teachers of technical specialities.

 

 

 

 

 

 

▲ An Introduction to Probability Theory and Mathematical Statistics. / V. M. Burlayenko, G. V. Rudnyeva, S. D. Dimitrova-Burlayenko. An introduction to probability theory and mathematical statistics : The textbook. – Kharkiv : NTU “KhPI”, 2013. – 264 p.

Authors: V. M. Burlayenko, G. V. Rudnyeva, S. D. Dimitrova-Burlayenko

This educational textbook contains theoretical material on probability theory alongside mathematical statistics. Main theorems and statements are proven and main formulas are derived necessary to solve the practical problems. Variants of typical tasks on considered subjects are proposed for individual work. The application of the material is illustrated by numerous examples and figures.

The textbook is recommended to students of technical specialities studying the course “Probability Theory and Mathematical Statistics” in English as well as foreign students and teachers of higher mathematics.

 

 

 

 

▲ Differential Equations and Series / L.V. Kurpa, O.S. Mazur, T.V. Shmatko. Differential equations and series: The textbook. – Kharkiv: NTU KhPI, 2013. – 288 pages.

Authors: L.V. Kurpa, O.S. Mazur, T.V. Shmatko

The textbook includes proofs of all essential theorems covered by the mathematical analysis curriculum, as well as problems recommended for classroom instruction with a teacher and for homework assignments. For each topic, variants of control tasks are provided. This manual is intended for both teachers and students of technical universities who use English to teach and learn higher mathematics courses.

 

 

 

 

 

▲  Mathematical analysis in examples and problems. Part 1 / . L. V. Kurpa, A.B. Linnik, T. V. Shmatko. Mathematical analysis in examples and problems. Part 1. – Kharkiv: NTU «KhPI», 2024. – 209 p.

Authors: L. V. Kurpa, A.B. Linnik, T. V. Shmatko.

The textbook provides concise theoretical material and practical tasks, including individual homework, from the following sections of mathematical analysis: the theory of limits, differential calculus for functions of one variable, indefinite integrals, definite integrals, and their application in solving geometric problems. It contains many problems to be solved both in practical classes and at home, covering the topics specified in the mathematical analysis work program.

This textbook is intended for students of technical specialties.

 

 

• You can download the book from the digital repository of NTU “KhPI”.

 

▲ Linear Algebra: the Textbook for Engineering Students /L. V. Kurpa, K. I. Liubytska, V. M. Burlayenko – Kharkiv : NTU «KhPI», 2024. – 154 p.

Authors: L. V. Kurpa, K. I. Liubytska, V. M. Burlayenko

This textbook provides theoretical content on linear algebra presented in English. It covers key concepts, statements, and formulas essential for a profound understanding and skill development in working with linear algebra. Additionally, numerous examples are included to illustrate the practical applications of the presented material, facilitating easier mastery of the concepts for students of technical specialties in all forms of education.

Tailored for students at technical universities, who are taking a linear algebra course in English. It’s also useful for foreign students and lecturers seeking assistance in developing their own lecture materials in higher technical educational institutions.

• • You can download the book from the digital repository of NTU “KhPI”.

 

 

 

▲ Normal Modes and Localization in Nonlinear Systems / Vakakis, A. F., Manevitch, L. I., Mikhlin, Y. v., Pilipchuk, V. N., and Zevin A. A.  Wiley, New York, 1996.

Authors: A.F. Vakakis, L.I. Manevitch, Yu.V. Mikhlin, V.N. Pilipchuk,     A.A. Zevin

This landmark volume offers a completely new angle on the study of vibrations in discrete or continuous nonlinear oscillators. It describes the use of NNMs to analyze the vibrations of nonlinear systems and design systems with motion confinement properties.

Normal Modes and Localization in Nonlinear Systems features

• • • New and established mathematical techniques that can be used for more refined vibration and shock isolation designs of practical flexible structures
    • Complete coverage of free and forced motions in systems with weak or strong nonlinearities, including results that cannot be captured with existing linear or quasi-linear techniques
    • A new method for analyzing strongly nonlinear systems that permits perturbation analysis of systems with essential nonlinearities
    • A theoretical link between nonlinear normal modes and standing solitary waves
    • The first experimental verifications of nonlinear mode localization and nonlinear motion confinement in flexible engineering structures

You can read this book on the site …