Zbierka úloh z matematickej analýzy III.

E-book

Vladimír Zeleňák (ed.)

Proceedings of Abstracts of the Student Scientific Conference of the Faculty of Science, Pavol Jozef Šafárik University in Košice

A characteristic feature of education at high-quality universities — among which the Faculty of Science at Pavol Jozef Šafárik University (UPJŠ) in Košice proudly belongs — is the close connection between education and scientific research. Students gain knowledge in their field of study not only through theoretical coursework in individual disciplines, but also through active involvement in solving specific scientific tasks as part of research teams. This can occur during the development of final theses or through participation in the Student Research Assistant Program (ŠPVS), which was revitalized at the faculty in 2015.

The Student Scientific Conference (ŠVK) is one of the faculty’s traditional events, organized during the Faculty’s Science Days as part of Sciencefest. By its very nature, it fits seamlessly into the aforementioned framework of combining education with research, and it has long enjoyed great popularity and student interest. In 2016, the conference featured presentations by 125 students of the Faculty of Science at UPJŠ in Košice, across 16 thematic sections. This collection of abstracts provides an overview of the focus and goals of the student projects. We believe it will serve as inspiration for other potential participants of future conferences and will also be of interest to the broader public, offering additional insight into the faculty's activities.

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Marcel Uhrin - Petr Benda -  Peter Kaňuch

Bats represent a unique group of mammals, characterised by different life strategies. They are the only mammals capable of active flight, which, combined with their almost exclusively nocturnal activity, has led to the evolution of specific adaptations. One of the most striking is echolocation, which enables them to orientate themselves perfectly in their surroundings in the dark. Bats are mainly native to the tropics, but have also colonised areas outside the tropics, which, has led to a complex phenological cycle with active phases and interruptions during hibernation, especially in temperate zones. In this diverse and species-rich group (almost 1,500 known species), there is a wide range of social organisation as well as feeding and roosting strategies. The textbook "Fundamentals of Chiropterology" brings the current state of knowledge about these extraordinary animals in eleven chapters and two appendices for the first time in the Slovak language.

E-book

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.

Download the e-book for free (pdf)

E-book

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.

Download the e-book for free (pdf)

E-book

Miroslav Almáši (ed.)

The book of abstracts from the conference "Porous Materials for Environmental Applications 2024" is a collection of contributions of the conference participants, which contain original results of their scientific and research activities. The conference was aimed to share new findings dealing with the preparation, characterization and application of porous materials in environmental fields.

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Danica Studenovská a kol. 

Táto zbierka úloh je určená poslucháčom Prírodovedeckej fakulty UPJŠ, ktorí sa v rámci predmetu Matematika I. zoznamujú s pojmami funkcie, limity, derivácie, integrálu a ich aplikáciami. Ide najmä o študentov nematematických odborov a učiteľských kombinácií, avšak táto zbierka je vhodná aj pre iných študentov a záujemcov o základy matematickej analýzy.

Autori

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Valéria Skřivánková - Martina Hančová

The publication is focused on discrete random processes, primarily on Markov chains, which have wide application in the field of economics and finance.

The textbook is divided into five chapters, the first of which serves as an introduction to random processes and provides definition, properties and classification of random processes in general. The second chapter discusses Markov chains with discrete time, including valuation of transitions between states and their optimal management. The third chapter focuses on special Markov chains with continuous time and emphasizes construction and solution to the system of Kolmogorov differential equations, which describe the dynamics of the process development. The last two chapters illustrate applications of Markov chains using examples of queuing system modeling and renewal theory.

Besides the explanation of basic terms, definitions and theorems with proofs, this textbook also provides number of solved examples to illustrate the discussed theory. Problem assignments are placed at the end of each chapter, so that readers can test their understanding of the content as they progress through the book. Solutions to all the problems and the list of references are provided at the end of the publication.

This textbook is primarily intented for students majoring in Economics and Financial Mathematics at the Faculty of Science of Pavol Jozef Šafárik University in Košice, and it covers content of the course “Random Proceses 1“ thought there. It might however serve also students from other schools in similar progams or professionals interested in this topic.

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Adriana Zeleňáková - Jozef Bednarčík

Recenzovaný zborník príspevkov z vedeckej konferencie NANOVIR

Hlavným cieľom vedeckej konferencie NANOVIR bola prezentácia vedeckých výsledkov, získaných počas riešenia projektu NANOVIR – Nanočastice pre riešenie diagnosticko- terapeutických problémov s COVID-19, spolufinancovaného z Európskeho Fondu Regionálneho Rozvoja v Operačnom Programe Integrovaná Infraštruktúra 2014 – 2020, ITMS: 313011AUW7. Projekt bol riešený v období 1.1.2021 – 30.6.2023 a bol podporený sumou 1 916 004,79 EUR. Spolupodieľali sa na ňom tri spoluriešiteľské organizácie: Univerzita Pavla Jozefa Šafárika v Košiciach ako hlavný riešiteľ, Univerzita veterinárskeho lekárstva a farmácie v Košiciach ako partner č. 1 a Ústav experimentálnej fyziky Slovenskej akadémie vied ako partner č. 2.

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 Ľubomír Panigaj - Peter Ľuptáčik 

(Náčrt systému a fylogenézy)

Učebný text je primárne určený pre študentov jednoodborového štúdia biológie a všeobecnej ekológie, ako aj odborom učiteľského štúdia v rôznych kombináciách s biológiou. Venuje sa v nich opisu jednotlivých skupín živočíchov, ich morfológiu a anatómiu ilustruje na obrazových materiáloch. K jednotlivým morfologickým a anatomickým štruktúram sa v texte nevyjadrujeme podrobnejšie, nakoľko text nadväzuje na predmet Porovnávacia morfológia živočíchov, kde na úrovni organológie boli tieto najvýznamnejšie štruktúry v rámci prednášok a cvičení detailne vysvetlené a opísané. Rozsah učebného textu nie je veľký, podávame v ňom základné minimum poznatkov, čo je podmienené jednak rozsahom predmetu, ktorý je len jednosemestrový, jednak tým, že ďalšie, špecializované predmety rozširujú spektrum poznatkov napr. na úrovni entomológie, hydrobiológie alebo pôdnej biológie. V zavere niektorých kapitol formulujeme niekoľko cvičných otázok, ktoré si študenti môžu na základe predchádzajúceho textu zodpovedať, s podobnými otázkami sa totiž môžu stretnúť na skúške alebo na štátniciach.

Autori

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Jana Shepa (ed.)

The book of abstracts from 7th International Conference on Novel Materials: Fundamentals and Applications, NFA 2023 is composed of contributions from the participants of this international conference. The conference consisted of 3 invited lecture and 40 abstracts of participants. The conference is focused on novel materials and its application in various research areas. All contributions are professionally processed and inspiring.

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E-book

Jana Shepa (ed.)

The book of abstracts from 6th International Conference on Nanomaterials: Fundamentals and Applications, NFA 2022 is composed of contributions from the participants of this international conference. The conference consisted of 4 invited lecture and 52 abstracts of participants. The conference is focused on nanotechnology and its application in various research areas. All contributions are professionally processed and inspiring.

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E-book

Gabriel Semanišin - Emil Hutňan - Jana Oleničová

The proceedings contain contributions from participants of the UNIFOS 2014 conference, University Information Systems in Košice, which took place from October 27 to 29, 2014.

ICT centers are important element that provide functioning and development hardware and software infrastructure at Slovak Universities. There are more differences between them in real position, management, personal sources and financing. ICT centers provide a wide range of services to large number of university users and they implement the policy of information security recently.

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Adriana Zeleňáková - Zuzana Ješková - Adela Kravčáková - Gabriela Fabriciová - Erik Čižmár - Róbert Tarasenko - Jaroslava Szűcsová - Ľuboš Nagy (eds.)

Zborník obsahuje abstrakty príspevkov účastníkov 14. česko - slovenskej študentskej vedeckej konferencie vo fyzike, ktorá sa konala 2.-3.mája 2024 na PF UPJŠ v Košiciach.

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Jana Špaková Raschmanová - Zuzana Kudličková - Kvetoslava Stanková

Organic chemistry plays a key role in our lives, from the pharmaceutical industry to the production of plastics and food additives. Additionally, it is essential in biochemistry, as it deals with the basic building blocks of living organisms, such as carbohydrates, lipids, proteins, and nucleic acids. One of the best ways to teach organic chemistry and increase students' interest in the subject is through conducting school experiments. This study material presents a collection of visually striking practical experiments in organic chemistry that will help students better understand the chemical processes and techniques used in the field. This electronic study material is supplemented with visual material, allowing students to verify the results of experiments and better understand the individual procedures. At the end of each section, there are questions to help assess the acquired knowledge and encourage deeper understanding of the experiments conducted.

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Marcel Uhrin - David Jandzik - Andrej Čerňanský - Michal Rindoš - Blanka Lehotská - Stanislav Danko - Ján Kautman - Peter Mikulíček - Peter Urban - Daniel Jablonski

Bibliographies provide basic scientific information, illustrate quality and intensity of research in a particular topic, area, or time, and thus help build a cultural-historical perspective of society’s appreciation of knowledge and education. Here we provide a bibliography of herpetological research in the region of Slovakia between the years 1791 and 2017. We collected 2,183 references authored by 1,453 different authors and covering all species of amphibians (18) and reptiles (13) occurring in Slovakia and, in addition, amphibian and reptile taxa occurring in 94 other countries.

Most of the contributions were published in popular magazines and non-indexed journals, while only about 12% of all references represent scientific articles from journals indexed in relevant scientific databases. The extensiveness of study on amphibians and reptiles has varied among different periods within the selected time frame. However, an obvious intensification in the field of herpetology can be observed, especially during the second half of the 20th century. While there have only been few professionals specialized in herpetology, an important role in promoting the research and conservation of amphibians and reptiles in Slovakia has been played by non-governmental organizations and hobbyists. The most frequent type of herpetological data in the referenced literature comes from faunistic research, followed by conservation and general information on herpetofauna, with the majority of published articles in indexed journals coming from the fields of palaeontology, phylogeography, and population genetics.

The presented bibliography is the first step towards building a solid base for future systematic herpetological research in the country and Central Europe.

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Stela Csachová, Ján Kaňuk - Alena Gessert, Ladislav Novotný, Štefan Gábor,Jozef Šupinský

This book addressed the inquiry-based learning and teaching with the support of geospatial technologies. Today, geospatial technologies are influencing geography teaching learning, particularly in secondary education. Theoretical framework gives the reader the insight to inquiry-based learning, with special focus on inquiry in geography. The one-by-one step of inquiry is analysed in detail. The major part of the book presents the eleven models of geography lessons, representing the subject content of physical, human and regional geographies, various levels of inquiry and use of different geospatial technologies. The readers are acquainted with the use of geographic information system (particularly Google Earth and ArcGIS online), web portals, webGIS, open data, mobile applications and new forms of 3D cartographic visualisation (virtual reality, 3D print, dynamic 3D map) in teaching geography. The lesson models were tested with the students to be geography teachers in school year 2021/2022. This books serves as resource mainly for undergraduate teacher students and in-service geography teachers.

Download e-book for free (pdf)

E-book

Vladimír Zeleňák (ed.)

Proceedings of Abstracts of the Student Scientific Conference of the Faculty of Science, Pavol Jozef Šafárik University in Košice

A characteristic feature of education at high-quality universities — among which the Faculty of Science at Pavol Jozef Šafárik University (UPJŠ) in Košice proudly belongs — is the close connection between education and scientific research. Students gain knowledge in their field of study not only through theoretical coursework in individual disciplines, but also through active involvement in solving specific scientific tasks as part of research teams. This can occur during the development of final theses or through participation in the Student Research Assistant Program (ŠPVS), which was revitalized at the faculty in 2015.

The Student Scientific Conference (ŠVK) is one of the faculty’s traditional events, organized during the Faculty’s Science Days as part of Sciencefest. By its very nature, it fits seamlessly into the aforementioned framework of combining education with research, and it has long enjoyed great popularity and student interest. In 2016, the conference featured presentations by 125 students of the Faculty of Science at UPJŠ in Košice, across 16 thematic sections. This collection of abstracts provides an overview of the focus and goals of the student projects. We believe it will serve as inspiration for other potential participants of future conferences and will also be of interest to the broader public, offering additional insight into the faculty's activities.

Download the e-book for free (pdf)

Marcel Uhrin - Petr Benda -  Peter Kaňuch

Bats represent a unique group of mammals, characterised by different life strategies. They are the only mammals capable of active flight, which, combined with their almost exclusively nocturnal activity, has led to the evolution of specific adaptations. One of the most striking is echolocation, which enables them to orientate themselves perfectly in their surroundings in the dark. Bats are mainly native to the tropics, but have also colonised areas outside the tropics, which, has led to a complex phenological cycle with active phases and interruptions during hibernation, especially in temperate zones. In this diverse and species-rich group (almost 1,500 known species), there is a wide range of social organisation as well as feeding and roosting strategies. The textbook "Fundamentals of Chiropterology" brings the current state of knowledge about these extraordinary animals in eleven chapters and two appendices for the first time in the Slovak language.

E-book

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.

Download the e-book for free (pdf)

E-book

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.

Download the e-book for free (pdf)

E-book

Miroslav Almáši (ed.)

The book of abstracts from the conference "Porous Materials for Environmental Applications 2024" is a collection of contributions of the conference participants, which contain original results of their scientific and research activities. The conference was aimed to share new findings dealing with the preparation, characterization and application of porous materials in environmental fields.

Download the e-book for free (pdf)