Zbierka úloh z matematiky pre nematematické odbory

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Ladislav Janovec

An enormous progress in computer technology, closely linked with advances in computational chemistry, has enabled the user to exploit the principles of quantum chemistry to elucidate the chemical phenomena.

Computational chemistry is the branch of science that requires, except an academic knowledge, software skills to fully exploit a potential of theoretical methods. The aim of this textbook is to help the user take the legendary first step in the field of computational chemistry to opening a new horizon of knowledge.

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E-book

Jozef Bednarčík (ed.)

Pavol Jozef Šafárik University in Košice under the auspices of Ministry of Education, Research, Development and Youth of the Slovak Republic, Ministry of Economy of the Slovak Republic and European X-Ray Free-Electron Laser Facility GmbH in Hamburg organizes School of XFEL and Synchrotron Radiation Users 2024 (SFEL 2024). The school is continuation of the Winter Schools of Synchrotron radiation held in 2011, 2013, 2014 and SFEL 2017, 2018, 2019 and 2022. The aim of the SFEL2024 school is to facilitate the growth of new Slovak research community of high expertise in high-efficiency RTG laser and synchrotron and neutron sources. The SFEL school is designed for efficient transfer of the rapidly developing know-how in these areas to young generation – researchers and university students. The next aim of the SFEL2024 is strengthening of personal connections between the local Slovak research community and forming scientific teams of XFEL users. Slovak research community thus can take advantage of the fact that Slovakia is a shareholder of European XFEL GmbH Company in Hamburg, but also makes more efficient use of other closely related scientific facilities, including ILL and ESRF in Grenoble and DESY in Hamburg.

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Alena Gessert

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Stanislav Lukáč - Ľubomír Šnajder - Ján Guniš - Zuzana Ješková

Publikácia je určená vedeckým pracovníkom v didaktike a učiteľom matematiky a informatiky. Našim zámerom je predstaviť čitateľom základnú orientáciu v problematike bádateľsky orientovaného vyučovania, vysvetliť a na ukážkach demonštrovať viaceré úrovne žiackeho bádania, poskytnúť klasifikáciu bádateľských zručností. Nosnou časťou publikácie sú metodiky pre bádateľsky orientované vyučovanie konkrétnych tém zo školskej matematiky a informatiky. Predkladáme námety na realizáciu bádateľských aktivít, aktívnu prácu s informáciami pri riešení rôznych typov problémov a aplikáciu moderných digitálnych technológií pri skúmaní a objavovaní zákonitostí. Do publikácie sme zaradili sedem metodík pre vyučovanie matematiky a osem metodík pre vyučovanie informatiky v 1. a 2 ročníku strednej školy.

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Prílohy

Danica Studenovská - Tomáš Madaras 

Táto publikácia je určená pre študentov nematematických odborov na Prírodovedeckej fakulte UPJŠ v Košiciach. Jej obsahom je látka preberaná v prvom semestri v rámci predmetu Matematika I..

Publikácia nadväzuje na učivo stredných škôl a nevyžaduje žiadne predbežné špeciálne znalosti. Môže slúžiť ako základ na ďalšie samostatné štúdium a môže byť užitočná aj pre iných záujemcov o matematiku a jej aplikácie.

Vyriešené príklady v jednotlivých kapitolách majú pomôcť čitateľovi pri zvládnutí štúdia. Tomu napomáhajú aj ilustratívne obrázky.

Autori

E-book

Renáta Oriňaková(ed.)

Trends in chemistry, research and education at Faculty of
Sciences of P.J. Šafárik University Košice

November 4, 2016, Faculty of Natural Sciences, Pavol Jozef Šafárik
University, Košice, Slovakia

Organized by:
Faculty of Natural Sciences
Pavol Jozef Šafárik University in Košice
Slovak Chemical Society

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Peter Fedoročko a kol. 

Vysokoškolský učebný text Prírodovedeckej fakulty UPJŠ.

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Ondrej Hutník

The concept of the integral is one of the most significant concepts in mathematics as a whole. In its most primitive form, it was already used by the ancient Greeks in the creation of Euclidean geometry. However, it was only after Descartes' work on analytical geometry in 1637 that mathematicians could begin to consider the integral as a subject of analysis. Descartes' work laid the groundwork for the discovery of infinitesimal calculus by Leibniz and Newton around 1665. At that time, a great dispute arose over the priority of this discovery, dividing scholars of Germany and England into two opposing camps, each favoring their own champion. Today, we know that Newton's work on fluxions and fluents was somewhat earlier, but Leibniz's notation and approach have gained more acceptance in the mathematical world, and the symbols ∫ ∫ and d d are still used today. A brief overview of the history of the integral will be presented in Chapter 1.

Today, there is a plethora of scripts, textbooks, and books dedicated to explaining the concept of the integral. Therefore, every potential author faces the initial question of whether to write another text on this topic. Our affirmative answer to this question was driven by the students' request to find the subject matter of a part of the winter semester of the second year presented in a coherent form. The second motivation is a slightly different approach to the topic. If we consider the methods typically used in solving problems and gaining routine with a certain integral, it mainly involves the Newton-Leibniz formula, and often there is little time left to compute the definite (Riemann) integral using its definition. Therefore, we included a discussion of the Newton integral in Chapter 2, which reflects this fact and is directly related to the indefinite integral, whose various calculation methods receive relatively much attention in the previous semester. Only after that, in Chapter 3, do we build the theory of the Riemann integral, present criteria for its existence, classes of integrable functions, basic properties, and finally its relationship with the Newton integral. Questions primarily concerning geometric applications are addressed in Chapter 4, and in the final chapter, we focus on extending the Riemann integral to unbounded functions and unbounded intervals.

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Gregor Bánó

Photonics is an application-oriented discipline at the interface of optics, opto-electronics and quantum optics. It includes classical optics extended by the description of physical phenomena and optical devices that rely on quantum (photon) nature of light.
The main objective of the Photonics course is to provide a comprehensive overview of essential optical and photonic phenomena routinely applied in experimental scientific research while working with various light sources (e.g. in the field of biophotonics). The first chapters are devoted to the description of light at different levels. The logical order of subsections in this part corresponds to the structure of the textbook: B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics. The following chapters contain a description of laser operation and an overview of selected optical instruments and their applications.
The body text is complemented by practical notes on the use of theoretical knowledge during daily work in the laboratory. The course of Photonics requires a basic knowledge of mathematics, electromagnetism and optics, and thus it is recommended to students who previously passed through the courses of the Bachelor's program in Physics.

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Norbert Kopčo

Neuroscience is an interdisciplinary field of science at the interface of biological, psychological and computer sciences, which aims to describe the functioning of the brain and mind. Computational and cognitive neuroscience are subfields of neuroscience focused on the study of information processing in the human and animal nervous systems, and on the theoretical description of the brain and mind. This university textbook contains several assignments that provide an overview of the methods used in computational and cognitive neuroscience, with an emphasis on mathematical modeling and on the behavioral study of cognitive processes. The textbook builds on the author's previous works.

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Božena Mihalíková - Ondrej Hutník - Jozef Kiseľák

The textbook is devoted to the mathematical analysis of infinite series of numbers and functions. It is intended for students of mathematics, physics and computer science, as well as interdisciplinary study of combination with mathematics. It contains a theoretical background for investigating the convergence of infinite series, expanding functions into power and Taylor series, as well as the use of these results in various problems of mathematics, physics, and computer science. Using the historical background the textbook clarifies the motivations and the need to introduce some key concepts and their further development. Basic concepts and statements are demonstrated on a large number of solved exercises, but it contains a number of exercises for independent practice. Several results are supplemented by dynamic animations executable in the electronic version of the textbook.

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Božena Mihalíková - Ján Ohriska

This text is intended for first-year students in 76-12-8 ‘General Education Teaching’ in combinations with mathematics. It is based on the authors' lectures and their more than ten years of experience in teaching this subject at the Faculty of Education of the University of Applied Sciences. When writing it, the authors tried to take into account the specificity of mathematics teaching studies.

The present teaching text was not written due to the lack of textbooks on mathematical analysis. The reason for writing it was the authors' findings that the students do not have sufficient experience in working with specialized literature from secondary school, the difficulties for many of them (especially in the first semesters) are caused by even a slightly different interpretation, not rarely also by a change in labeling, which makes them miss the essence of the studied problem. The authors of the text did not set out to be original. Their aim was to make such a selection of topics as is necessary for a future teacher of mathematics and to choose such a method of interpretation which, in their opinion, is suitable for first-year students.

A good mastery of the curriculum (expansion of the mathematical apparatus and the related possibilities of applying other methods of proof as well as the acquisition of the necessary numerical skills) presupposes the use of other literary sources (textbooks, collections of problems) according to the teacher's recommendation.

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Vladimír Sedlák

The university textbooks entitled Global Navigation Satellite Systems: GPS, GLONAS, Galileo, Compass present four navigation systems of the GNSS (Global Navigation Satellite Systems): American NAVSTAR GPS, Russian GLONASS, European Galileo and Chinese Compass. The Satellite-Based Augmentation Systems (SBAS) are also briefly explained. They provide regional service in augmenting the reach and support of signals from satellites of the GNSS (GPS, GLONASS, Galileo, Compass). Each satellite navigation system in the frame of GNSS is elucidated in terms of its principles of operation, structure, specificities, applications, and future perspectives.

The university textbook aims to improve the reader’s understanding of the principles and activities of the presented GNSS. The book emphasizes the possibilities of GNSS applications in geodesy and geography. The university textbook constitutes the basic study literature for the class Global Navigation Satellite Systems within the study program Geography and Geoinformatics at the Faculty of Science of the Pavol Jozef Šafárik University in Košice. For a deeper study of the GNSS issue, it is necessary to extend the study materials to include other educational scientific literature dealing with navigation satellite systems and their applications.

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Daniel Klein

Statistics is defined as a scientific discipline based on learning from data and on finding, controlling, and presenting uncertainty. In these university textbooks we present the history of statistics, basic concepts of statistical modeling, measurement of dependencies, regression models, analysis of variance. We describe simple sorting, multiple comparisons, assumptions of the ANOVA model, Kruskal-Wallis test.

University textbooks are suitable for students of mathematics and computer science at the first and second level of universities. Study materials are also suitable for students of non-informatics disciplines with a view to improving their knowledge and practical experience in the fields of informatics and provide an opportunity for students to apply in IT companies in solving practical tasks.

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Erik Čižmár

Textbook Automation of Laboratory Experiments in LabVIEW environment is devoted to the basics of graphical programming and shows the way how to communicate with measuring equipment and Arduino development boards in LabVIEW. The basic concepts of creating a virtual instrument and its interactive user environment are introduced. Three physical tasks are presented, the practical implementation of which takes place with the use appropriate instrumentation and LabVIEW. Practical tasks are dedicated to measuring the transmission characteristics of a low-pass RC filter, measuring the natural resonant frequency of a quartz tuning fork using the heterodyne pulse method, and mapping the magnetic field of a permanent magnet using Arduino.

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Zuzana Vargová - Miroslav Almáši - Juraj Kuchár - Jana Dinajová 

The script „Základné laboratórne praktikum z anorganickej chémie“ builds on previous editions of the script, with some thematic units updated and supplemented with new knowledge, principles, and detailed work procedures.

This script is intended as a teaching aid for first-year students of the chemistry and interdisciplinary study programs at the Faculty of Science, Pavol Jozef Šafárik University in Košice. The introductory part of the volume acquaints students with safety regulations that they should follow during work in a chemical laboratory. Subsequently, in five chapters, basic laboratory techniques are described in detail, which students will use in the further part of the practices for preparing inorganic compounds. These chapters are enriched with illustrative images created using the freely distributable ACDFreeLabs 10 program or taken from literature listed at the end of the script. Some images were created by the authors, and others were taken from the catalog of Fisher Slovakia, s.r.o., which provided written permission for their use. The chapters describing the preparation of inorganic compounds are organized according to their composition, from simple elements or molecules, through binary compounds, acids, and salts, to complex compounds.

Within this subject, students should apply their theoretical knowledge gained during lectures on General Chemistry and Inorganic Chemistry and thereby acquire basic practical experience and skills that they will use in further studies.

The last two chapters were developed based on cooperation with Duslo a.s., Production Plant Strážske, which participates in the innovation of practical teaching through direct involvement of experts from practice as part of the KEGA project No. 008UPJŠ-4/2018.

Authors

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E-book

Ladislav Janovec

An enormous progress in computer technology, closely linked with advances in computational chemistry, has enabled the user to exploit the principles of quantum chemistry to elucidate the chemical phenomena.

Computational chemistry is the branch of science that requires, except an academic knowledge, software skills to fully exploit a potential of theoretical methods. The aim of this textbook is to help the user take the legendary first step in the field of computational chemistry to opening a new horizon of knowledge.

Download the e-book for free (pdf)

E-book

Jozef Bednarčík (ed.)

Pavol Jozef Šafárik University in Košice under the auspices of Ministry of Education, Research, Development and Youth of the Slovak Republic, Ministry of Economy of the Slovak Republic and European X-Ray Free-Electron Laser Facility GmbH in Hamburg organizes School of XFEL and Synchrotron Radiation Users 2024 (SFEL 2024). The school is continuation of the Winter Schools of Synchrotron radiation held in 2011, 2013, 2014 and SFEL 2017, 2018, 2019 and 2022. The aim of the SFEL2024 school is to facilitate the growth of new Slovak research community of high expertise in high-efficiency RTG laser and synchrotron and neutron sources. The SFEL school is designed for efficient transfer of the rapidly developing know-how in these areas to young generation – researchers and university students. The next aim of the SFEL2024 is strengthening of personal connections between the local Slovak research community and forming scientific teams of XFEL users. Slovak research community thus can take advantage of the fact that Slovakia is a shareholder of European XFEL GmbH Company in Hamburg, but also makes more efficient use of other closely related scientific facilities, including ILL and ESRF in Grenoble and DESY in Hamburg.

Download the e-book for free (pdf)

E-book

Alena Gessert

Download e-book for free (pdf)

E-book

Stanislav Lukáč - Ľubomír Šnajder - Ján Guniš - Zuzana Ješková

Publikácia je určená vedeckým pracovníkom v didaktike a učiteľom matematiky a informatiky. Našim zámerom je predstaviť čitateľom základnú orientáciu v problematike bádateľsky orientovaného vyučovania, vysvetliť a na ukážkach demonštrovať viaceré úrovne žiackeho bádania, poskytnúť klasifikáciu bádateľských zručností. Nosnou časťou publikácie sú metodiky pre bádateľsky orientované vyučovanie konkrétnych tém zo školskej matematiky a informatiky. Predkladáme námety na realizáciu bádateľských aktivít, aktívnu prácu s informáciami pri riešení rôznych typov problémov a aplikáciu moderných digitálnych technológií pri skúmaní a objavovaní zákonitostí. Do publikácie sme zaradili sedem metodík pre vyučovanie matematiky a osem metodík pre vyučovanie informatiky v 1. a 2 ročníku strednej školy.

Download the e-book for free (pdf)

Prílohy

Danica Studenovská - Tomáš Madaras 

Táto publikácia je určená pre študentov nematematických odborov na Prírodovedeckej fakulte UPJŠ v Košiciach. Jej obsahom je látka preberaná v prvom semestri v rámci predmetu Matematika I..

Publikácia nadväzuje na učivo stredných škôl a nevyžaduje žiadne predbežné špeciálne znalosti. Môže slúžiť ako základ na ďalšie samostatné štúdium a môže byť užitočná aj pre iných záujemcov o matematiku a jej aplikácie.

Vyriešené príklady v jednotlivých kapitolách majú pomôcť čitateľovi pri zvládnutí štúdia. Tomu napomáhajú aj ilustratívne obrázky.

Autori