scholarly journals Development of ICT competence among students when teaching inverse problems for differential equations with the use of computer technology

2019 ◽  
Vol 16 (4) ◽  
pp. 328-337
Author(s):  
Viktor S. Kornilov
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Computer Technology ◽  
Three Dimensional ◽  
Theory And Practice ◽  
Computational Mathematics ◽  
Modern Computer ◽  
Computer Technologies ◽  
Ict Competence

Problem and goal. The great need to apply the theory of inverse problems for differential equations (IP) in the research of applied problems is explained by the fact that it is possible to effectively study hard-to-reach or inaccessible objects and processes, to identify, for example, the location of objects, determine their shape, etc. In addition, it is possible to identify causeand-effect relationships of processes and phenomena (see, for example, [5; 6; 8; 11; 14; 17; 19]). It became possible, in many respects, thanks to modern computer technologies which allow to investigate various mathematical models of inverse problems, realize modern computational algorithms of the numerical solution of inverse problems for differential equations, carry out three-dimensional visualization of their decisions and control of accuracy of calculations. This circumstance explains the widespread introduction of modern computer technologies in the process of teaching students of IP educational institutions of physics and mathematics (see, for example, [2; 5; 6; 8; 10-14; 17; 19; 20]). In the process of teaching, goals are set to ensure that students form a system of fundamental knowledge in the field of theory and practice of inverse problems, applied and computational mathematics, acquire the skills to choose and apply computer technology to find solutions to inverse problems, develop their ICT competence. Methodology. The development of ICT competence among students of universities of physical and mathematical areas of training, as a result of learning IP, is ensured by how successfully the conditions will be implemented in practice, including: 1) involvement of specialists in the field of inverse problems for differential equations with experience in the use of computer technology in the study of inverse problems; 2) conducting lectures and practical classes using multimedia and computer technologies; 3) implementation of didactic principles of teaching inverse problems for differential equations using computer technologies; 4) attraction of students to performance of semester tasks, course and final qualifying works on inverse problems for differential equations with use of computer technologies. Results. In practical classes, students acquire the skills to apply modern computer technology in the study of IP. Students gain experience in analyzing new information about the studied physical processes and phenomena using computer technology. Students form knowledge about the role of computer technology in mobile research of mathematical models of inverse problems for differential equations, demonstrating ICT competence. Conclusion. Developed in the process of teaching inverse problems for differential equations using computer technologies, ICT competence will obviously allow students in their future professional activities to effectively apply a variety of computer technologies in the study of mathematical models of inverse problems.

scholarly journals The development of scientific outlook of students when teaching inverse problems for differential equations

2019 ◽  
Vol 16 (1) ◽  
pp. 46-55
Author(s):  
Viktor Semenovich Kornilov
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Research Work ◽  
Teaching Experience ◽  
Physical Processes ◽  
Mathematical Methods ◽  
Important Place ◽  
The World ◽  
Scientific Worldview

Problem and goal. Modern achievements of the world Science of nature and the world, physical laws and laws should be disclosed at an accessible level to University students. Among the scientific methods of research of physical processes and phenomena, an important place is the method of mathematical modeling, because mathematical models have scientific and cognitive potential and versatility (see, for example, [2-4]). The use of mathematical models of inverse problems for differential equations (IPDE) allows to effectively investigate many processes and phenomena occurring in the air, earth and water environment. It is not surprising that in some Russian universities in the physical and mathematical areas of training are taught IPDE in the form of a choice of courses. The goals and objectives of such teaching are set, as a result of which students would develop creative mathematical abilities, formed fundamental knowledge in the field of physical education, developed a scientific worldview. Methodology. The development of scientific outlook of students of physical and mathematical directions of preparation, as a result of teaching IPDE, ensured the successful will be implemented in practice, such conditions as: 1. the involvement of experts in the field IPDE with teaching experience at the university; 2. development of the content of lectures and practical classes on the basis of modern achievements of the theory of inverse and incorrect problems, taking into account the professional orientation of training students; 3. the implementation of the principles, methods and means of education IPDE; 4. involvement of students in research work in scientific seminars and participation in scientific conferences devoted to IPDE; 5. implementation of methodological approaches that allow students to develop the skills and abilities of independent analysis of applied and humanitarian nature of the results of research of IPDE. Results. In practical classes on the IPDE students acquire the ability and skills to apply effective approaches and mathematical methods of finding solutions to inverse problems, followed by a logical analysis of their solutions. As a result, students gain useful experience in the analysis of new information about the studied physical processes and phenomena, form new scientific knowledge about the world on the basis of which develop a scientific worldview. Conclusion. Developed, in the process of teaching IPDE, the scientific outlook helps students to understand that mathematical models IPDE are relevant to theory, experiment and philosophy - the basic methods of knowledge researchers; to understand the humanitarian value of mathematical models IPDE.

scholarly journals КЛАССИФИКАЦИЯ ВОЗМОЖНЫХ ЗАДАЧ ДЛЯ ИССЛЕДОВАНИЯ НЕЛИНЕЙНЫХ ВОЛН В НАСЫЩЕННЫХ ПОРИСТЫХ СРЕДАХ

2021 ◽  
Vol 7 (3(57)) ◽  
pp. 34-39
Author(s):  
Ш.А. КЕРИМОВА
Keyword(s):  
Water Resources ◽  
Computer Technology ◽  
Natural Environment ◽  
The State ◽  
Highly Qualified ◽  
Drainage Basins ◽  
Rational Use ◽  
Modern Computer ◽  
Computer Technologies ◽  
Household Activities

Применение вычислительной техники и современных компьютерных технологий для анализа состояния гидроэкосистем открывает новые возможности как перед учеными-исследователями, так и перед лицами и организациями, принимающими ответственные решения по рациональному использованию природной среды на благо человека, а также поддержки решений в отношении осуществления мероприятий во всех видах хозяйственной и культурно-бытовой деятельности с использованием водных ресурсов и водосборных бассейнов путем формирования высококвалифицированных рекомендаций [1]. Abstarct. The use of computer technology and modern computer technologies for analyzing the state of hydroecosystems opens up new opportunities both for scientists-researchers and for persons and organizations making responsible decisions on the rational use of the natural environment for the benefit of humans, as well as support for decisions regarding the implementation of measures in all types economic and cultural and household activities using water resources and drainage basins by forming highly qualified recommendations [1].

Using Tests, Modern Computer Technologies and Information Processing in Systems Diagnostics and Prevention of Addictive Behavior (short review)

2015 ◽  
Vol 22 (3) ◽  
pp. 177-182
Author(s):  
Калиниченко ◽  
O. Kalinichenko
Keyword(s):  
Computer Technology ◽  
Short Review ◽  
Test Methods ◽  
Addictive Behavior ◽  
Diagnostic Tools ◽  
Biological Factors ◽  
Validity And Reliability ◽  
Modern Computer ◽  
Computer Technologies ◽  
Health Promoting

This article discusses the possibility of the effectiveness of the application of diagnostic methodologies to identify the propensity to addiction, examines the possibility of using modern computer technologies in the diagnosis and prevention of addiction, the formation of health-promoting behaviours. The author presents a review of modern tests, computer programs and computer technology that allows not only to evaluate the likely risk of addictive behavior, but also to suggest corrective measures with regard to personal, social, biological factors influencing the formation of addictive behavior. Each of the analyzed test methods is based on a large theoretical and empirical base. Test methods were tested for validity and reliability, and offer computer technologies and systems of processing of the received information are detailed instructions. The author has made an attempt to classify a number of methods and technologies for diagnosis of deviant forms of behaviour, to highlight their specificity, to identify opportunities and constraints. Studied computer techniques and traditional tests can be used as an independent diagnostic tools of various types of addictive behavior, can be included in the scorecard addicting behavior in general.

scholarly journals A new structure to n-dimensional trigonometric cubic B-spline functions for solving n-dimensional partial differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
K. R. Raslan ◽  
Khalid K. Ali ◽  
Mohamed S. Mohamed ◽  
Adel R. Hadhoud
Keyword(s):  
Partial Differential Equations ◽  
Numerical Methods ◽  
Differential Equations ◽  
Mathematical Models ◽  
Three Dimensional ◽  
Spline Functions ◽  
Test Problems ◽  
Spline Collocation ◽  
Partial Differential ◽  
B Spline

AbstractIn this paper, we present a new structure of the n-dimensional trigonometric cubic B-spline collocation algorithm, which we show in three different formats: one-, two-, and three-dimensional. These constructs are critical for solving mathematical models in different fields. We illustrate the efficiency and accuracy of the proposed method by its application to a few two- and three-dimensional test problems. We use other numerical methods available in the literature to make comparisons.

scholarly journals The use of modern computer technology to determine the possibility of acclimatization of adventitious phytophages in Ukraine during the analysis of phytosanitary risk (РRA)

2018 ◽  
pp. 3-10
Author(s):  
А. Borzykh ◽  
Yu. Klechkovsky ◽  
L. Titova ◽  
O. Palagina
Keyword(s):  
Computer Technology ◽  
Host Plants ◽  
Computer Programs ◽  
Modern Computer ◽  
Computer Technologies ◽  
Thaumatotibia Leucotreta ◽  
Short Time ◽  
Modern Computer Technology ◽  
Lemon Tree

The article contains information on the use of modern computer technologies to determine the possibility of acclimatization of adventitious phytophages in Ukraine during the analysis of phytosanitary risk. The use of modern computer programs Agro Atlas, MapInfo v.11.0 and Idrisi Taiga allowed in a short time to analyze the availability of fodder base (host plants) and the correspondence of ecoclimatic conditions of Ukraine, as AРR region, to the corresponding indicators of the modern range of pests and to identify potential acclimatization zones for Oemona hirta (lemon tree borer) and Thaumatotibia leucotreta (false apple moth).

Digitized

2012 ◽  
Author(s):  
Peter J. Bentley
Keyword(s):  
Computer Technology ◽  
User Interfaces ◽  
Popular Science ◽  
Theory And Practice ◽  
The Internet ◽  
General Reader ◽  
Mobile Phone Networks ◽  
Open The Doors ◽  
Dot Com ◽  
Current Stage

There's a hidden science that affects every part of your life, a science so powerful that you would be hard-pressed to find a single human being on the planet unaffected by its achievements. It is the science behind computers, the machines which drive the supply and creation of power, food, medicine, money, communication, entertainment, and most goods our stores. It has transformed societies with the Internet, the digitization of information, mobile phone networks, and GPS technologies. Written in friendly and approachable language, Digitized provides a window onto the mysterious field from which all computer technology originates, making the theory and practice of computation understandable to the general reader. This popular science book explains how and why computers were invented, how they work, and what will happen in the future. Written by a leading computer scientist, Peter J. Bentley, it tells this fascinating story using the voices of pioneers and leading experts interviewed for the book, in effect throwing open the doors of the most cutting-edge computer laboratories. Bentley explores how this young discipline grew from the early work by pioneers such as Turing, through its growth spurts in the Internet, its difficult adolescent stage where the promises of AI were never achieved and dot-com bubble burst, to its current stage as a semi-mature field, capable of remarkable achievements. Packed with real-world examples, Digitized is the only book to explain the origins and key advances in all areas of computing: theory, hardware, software, Internet, user interfaces, virtual reality, and artificial intelligence. If you have an interest in computers--whether you work with them, use them for fun, or are being taught about them in school--this book will provide an entertaining introduction to the science that's changing the world.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

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