The present paper describes the fact that revised and pedagogically justifiable implementation of CAS systems (e.g. Matlab system) is a great contribution to teaching higher mathematics. It brings practical applications to mathematics teaching and thus enhances motivation and students’ interest in the discussed topic. The Computer Algebra System, popularly known as CAS, is a modern computing technology that provides great learning and teaching opportunities to both students as well as instructors. MATLAB is one of the most popular CAS programs that is widely used in mathematics classrooms especially at the university level. As more and more universities are adopting its use in education, it is necessary to study and analyze how the software could be used in teaching and learning of mathematics. It has been shown to be a technology that could be used for developing mathematical thinking, concepts and skills, and a source of motivating students for learning mathematics. It is also a very useful tool in demonstrating connections in various underlying mathematical concepts in the teaching and learning processes.
Vol. 4 (2020), Issue 2
Table of Contents
THEORETICAL FOUNDATIONS AND SPECIFICITY OF MATHEMATICAL MODELLING
Comparative analysis of pseudorandom sequences using modified Barker codes and M – sequences of the same lengthpg(s) 45-50
The paper discusses the correlation properties of pseudo-random sequences (PRS) used to form noise-like signals in high-speed data transmission systems. The most frequently used pseudo-random sequences are considered: modified Barker codes, M-sequences having the same length. In the Matlab medium a comparative analysis of the correlation properties of the PRS is done. It is shown, that modified Barker codes have unsatisfactory correlation properties. It is proved, that the use of M – sequences allows to obtain signals with the required correlation properties for communication systems, including systems with code division of channels. The directions of further research are determined.
This article discusses the problems of teaching non-standard tasks at school. Currently, one of the main tasks of secondary schools is to identify creative thinking abilities of students and solve problems of their development. The report was identified as the main tool for developing students ‘ mental and thinking abilities. Problem solving is the most productive form of learning mathematics, and this process should be a necessary component of all extracurricular activities conducted in mathematics. Problems at the mathematical Olympiad are non-standard problems. Olympic tasks will usually help you learn a lot, find independent non-standard methods of solving problems. The high school curriculum provides for the use of the definition of inequality, proving using known inequalities, using the relationship between the arithmetic mean and geometric mean of positive numbers, and proving them using methods other than reverse-trip methods
MATHEMATICAL MODELLING OF TECHNOLOGICAL PROCESSES AND SYSTEMS
The main features of creating an information model (Digital Twin) for a technically complicated item are formulated. These include: a multitude of systemic representations of the item, individualization of its behavior and state under specific operating conditions, fatal uncertainty in the description of component properties, reconstruction of data based on sensors readings, individual lifetime expense in operation. Above features are illustrated by authors’ developments in application to power transmissions. The key issues of synthesis, calculation, design and diagnostics of transmissions based on the created complex of lifetime-and-functional models are solved. Transmission is considered as a multicomponent system with a variable structure and states. Creating a single universal model to reproduce basic properties of the technically complicated item is impossible. Principles of constructing models and methods for calculating, monitoring and predicting functional and lifetime properties are described. The basic representations of the transmission (structure, regular mechanical system, kinematic and dynamic diagrams, diagnostic model, schemes of limiting states, lifetime expense model) and the mathematical models serving them are developed. The approaches considered are methodologically typical for complex mechanical and combined objects based on mechanical systems.
Research, optimization and practical implementation of a Small Hydropower Plants as a source of clean electricity are one of the actual tasks in the current energetics, which is virtually impossible to solve without powerful computer support due to the strongly nonlinear nature of such systems. The article presents an overview of the most common simulation model schemes of Small Hydropower Plants, whereas explores the sub-models of its individual subsystems. The hydraulic turbine is considered as a core of the hydropower plant, whose efficiency calculation is analytically demanding and dependent on parameters that are often obtained only by theoretical estimation. In the article a fuzzy system was used to create its model based on measured operating data on the turbine flow rate and the height of its water column without the need to know the turbine parameters. Such a model is applicable in practice for the design of an energy-optimized hydroturbine control as well as to the effective determination of the deterioration rate. The correctness of the results was verified by simulation measurements in the MATLAB program.
Development of a simulation model of an information-measuring system of electrical characteristics of the functional coatings of electronic devicespg(s) 68-71
The article develops a simulation model (based on the MatLab Simulink mathematical processor) of an information-measuring system of electrical characteristics (residual surface electric charge, surface layer capacity, etc.) of functional coatings of electronic devices. The main purpose of the simulation model was to determine the rational parameters of measurement and control of the informationmeasuring system developed by the authors, which would simplify the process of setting up such a system, as well as explore the dynamic modes of its operation. The main advantage of the developed simulation model is the ability to conduct an interactive study of the operation of the information-measuring system under various, including limiting, modes. Tests of the simulation model of the information-measuring system made it possible to study its operation under various conditions and modes of the measurement experiment, as well as to virtually determine the rational operating parameters of such a measurement and control system. A satisfactory discrepancy of 8-11,5% was established for the experimental results compared with the data obtained analytically, which proves the correctness and adequacy of the compiled model.
Тhe article deals with probabilistic and statistical models of vibration processes. The covariance moment is considered. A dimensionless normalized covariance is introduced. To evaluate these theoretical characteristics, we used a statistical set of observational data. Observations that are cleared of measurement errors are combined into a sample of a specific volume. Random processes in vibration analysis are considered in detail. The characteristics of random processes are given: attenuation with a random beginning, a linear process with a random slope, and a harmonic process with a random amplitude. A statistical model of a linear system based on observations of input and output vibration processes is considered in detail.