Určitý integrál

Ondrej Hutník a kol. 

Zbierka úloh z matematickej analýzy III. je pokračovaním predchádzajúcich dvoch vydaných zbierok autorov Kulcsár a Kulcsárová. Táto časť obsahuje príklady na zopakovanie a precvičenie učiva stredných škôl, ako aj časti prvého semestra kurzu matematická analýza určeného pre študentov matematiky, fyziky, informatiky a učiteľského štúdia v kombinácii s matematikou. Zbierka môže tiež pomôcť všetkým učiteľom, ktorí chcú použiť rôzne úlohy vo svojom vyučovaní. Zbierka zahŕňa oblasť postupností reálnych čísel: aritmetické a geometrické postupnosti, všeobecne a rekurentne zadané postupnosti, nachádzajú sa tu úlohy na vyšetrovanie vlastností postupností (monotónnosť, ohraničenosť, konvergencia) a výpočet rôznych typov limít. Všetky zadané úlohy sú vyriešené na konci každej kapitoly s podrobným komentárom.

Autori

E-book

Ján Guniš - Ľubomír Šnajder

Prílohy

College scripts Programming in Python 1 are intended for future teachers of computer science. The content of the course is related to the teaching of programming in Scratch and is an introduction to text-based programming in Python.

Programming is introduced as a means of developing problem-solving skills. The first chapter is devoted to problem solving. The next 12 chapters sequentially introduce basic language constructions, data structures, and selected types of algorithms. Each of these chapters begins with an introduction to the problem. This section is primarily intended for self-study, to prepare students for the exercises. The following subchapter summarizes and completes the knowledge, and additional insights and approaches related to the chapter topic are presented. The chapters include a collection of exercises designed to practice and deepen knowledge and skills on the topic.

The final part of the chapter presents the solved problems. This section serves as a guide to solving the problems in the collection.

i

Download the e-book for free (pdf)

E-book

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.

Download the e-book for free (pdf)

E-book

Andrej Mock

The structure of the animal body is extremely varied. Each species has its distinctive morphological features, which bears as a testimony to long-term development and belonging to the developmental lineage. At the same time, the body has been tested for a long time by natural conditions, resulting in unique adaptations to the environment and life strategy. Despite this admirable variety - which includes both recent and fossil animals and which we have far from mapped – a comparison of body parts brings knowledge we can generalize: the main building principles, and boundaries within which phenotypic diversity is realized.

Comparative animal morphology today uses the latest methodological material and knowledge from other disciplines, from genetics, molecular biology and experimental embryology, through progressive imaging methods (e.g. electron microscopy, computer micro-tomography) and the possibilities of subsequent software processing of image material (measurement, staining, etc.) to the view of physics, chemistry, statics and geometry on the structures (to nanostructures) of the living body. Detailed knowledge of historical and contemporary conditions on Earth is an important interpretative context in the study of animal morphology. Surprisingly, the knowledge accumulated after centuries of research is now rapidly supplemented by new knowledge, and often the traditional knowledge is subsequently reinterpreted. Finally, and no less important, in studying animal (and human) morphology, we learn surprising knowledge about ourselves.

The author of the presented textbook had the ambition in a simplified form to introduce the reader, especially the student of biological studies, into a dynamic and fascinating scientific discipline, as the current comparative animal morphology is.

Stiahnite si e-knihu zadarmo (pdf)

E-book

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.

Download the e-book for free (pdf)

E-book

Rastislav Varga

The movement of domain walls in ferromagnetic materials is utilized in various magnetic devices for storing, processing, or transmitting signals and information. This mainly includes transformer cores, various sensors, memory devices (e.g., HDDs in PCs), as well as modern spintronic devices such as Racetrack memories, domain wall motion-based electronics, and so on.

This book is intended to serve as a textbook for advanced courses in the field of magnetic materials. It is primarily aimed at students interested in studying magnetic materials, as well as professionals from various fields who wish to understand the basics of domain structure and its changes. It is divided into nine chapters. The first chapter deals with a brief history of the study of domain structure in magnetic materials. The second chapter provides an introduction to the causes and manifestations of magnetic anisotropies. The third and fourth chapters are devoted to the causes of domain structure formation and domain walls. The fifth chapter discusses the structure of domain walls, their potential, and the critical field required for domain wall movement. The sixth chapter is dedicated to magnetization processes, one of which - domain wall movement - is discussed in detail in chapter 7. The eighth chapter contains a theoretical solution for domain wall movement. The final ninth chapter presents a modern method of domain wall movement induced by electric current.

The presented work assumes that the reader has at least basic knowledge in the field of magnetism. Otherwise, the author refers the reader to basic literature (e.g., [2.1 - 2.6]).

Download the e-book for free (pdf)

E-book

Jozef Bednarčík (ed.)

The SFEL school is continuation of the Winter Schools of Synchrotron radiation held in 2011, 2013, 2014 and SFEL 2017, 2018 and 2019. All schools of the series were held here, in Liptovský Ján, where our conference venue offers conditions for friendly and creative atmosphere.

The aim of the SFEL 2022 school is to facilitate the growth of a new Slovak research community with high expertise in the area of high-efficiency RTG laser, synchrotron and neutron sources. The SFEL school is designed for efficient transfer of the rapidly developing know-howin these areas to young generation – researchers and university students. The next aim of the SFEL2022 is strengthening of personal connections between the local Slovak research community and actually forming scientific teams of XFEL users, scientific teams of synchrotron or neutron sources users, respectively.

Slovak research community thus can take advantage of the fact that Slovakia is a shareholder of the 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

Janka Vrláková - Adela Kravčáková - Stanislav Vokál

The presented "Collection of Problems in Atomic and Nuclear Physics" is intended as a basic study material for lectures in General Physics IV in the second year of the bachelor's single-subject physics program and interdisciplinary studies combined with physics at the Faculty of Science of P. J. Šafárik University in Košice.

Its aim is to support independent student work and to deepen the acquired knowledge from the given physics course by solving selected problems. It is divided into three main parts: Atomic Physics, Nuclear Physics, and Experimental Methods of Nuclear Physics.

Each thematic chapter contains an overview of basic concepts, relations, and formulas necessary for better understanding of sample problems and for solving the attached set of unsolved problems.

Download the e-book for free (pdf)

E-book

Michal Jaščur

This is a supporting text for the undergraduate students interested in quan- tum theory of magnetism. The text represents an introduction to various theoretical approaches used in this eld. It is an open material, in the sense that it will be supported by appropriate problems to be solved by student at seminars and also as a homework.

The text consists of four chapters that form closed themes of the in- troductory quantum theory of magnetism. In the rst part we explain the quantum origin of the magnetism illustrating the appearance of the ex- change interaction for the case of hydrogen molecule. The second chapter is devoted to the application of the Bogolyubov inequality to the Heisenberg model and it represents the part which is usually missing in the textbooks of magnetism. The third chapter deals with the standard spin wave-theory including the Bloch and Holstein-Primakoff a approach. Finally, we discuss the application of the Jordan-Wigner transformation to one-dimensional spin-1/2 XY model.

The primary ambition of this supportive text is to explain diverse math- ematical methods and their applications in the quantum theory of mag- netism. The text is written in the form which should be sufficient to de- velop the skills of the students up to the very high level. In fact, it is expected that students following this course will able to make their own original applications of the methods presented in this book.

Download the e-book for free (pdf)

 Andrej Oriňak - Renáta Oriňaková - Andrea Fedorková

Nanotechnology represent the fastest developing science in the present. They are based on the technologies that enable the matter manipulation at atomic level. Nanotechnology offer prepartion of the new materials with unknown and very specific properties and functions.Recent nanotechnology still stay in formative phase of their development. But more and more they are visible with nano-specific phenomenons in the fundamental control of the properties as well mater behaviour. This is quite possible that without nanotechnology will not work any science to the future, moreover that science will not exist anymore. Nanotechnolgy will give a chance and force to transform world to more environmental and comfortable. Expected is expansion of the nanotechnolgy to molecular nanosystems – heterogenous nets, in which molecules and supramolecules work as the nanodevices. The computers and robots will be reduced to the small and ultrasmall dimensions. In medicine will foremost the application of nanotechnology in genetic therapy and elimination of ageing. Nanosurgery will work at molecular level, cancer cells will be identified early and filtered , then substituted with healthy and unchanged. It is necessary to inform university or high school students  about principles of nanotechnolgy, preparation of the nanostructures, functionality of them and to offer full representation about molecular systems and nanodevices; the methods of nanostructures characterization and about application in miniaturized systems. 

Authors

E-book

Renáta Oriňaková

We have prepared a publication that focuses on the personalities of professors. These personalities represent entire scientific teams, participated in the creation of new study programs, and had a significant impact on the formation of the faculty. Factually, we tried to capture the basic data in a uniform structure. We are building on a similar publication from ten years ago, which greatly helped us, especially with professors who worked at the faculty many years ago and whose memories are gradually fading. The ambition of the publication is to contribute to the preservation of basic information that is closely related to the history of the faculty.

doc. RNDr. Roman Soták, PhD. Dean of the Faculty of Science, UPJŠ in Košice

Download e-book for free (pdf)

E-book

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.

Download the e-book for free (pdf)

E-book

Rudolf Gális

The presented work provides basic knowledge of astronomy and astrophysics in a completely new multimedia format. The scope of the knowledge presented is mainly focused on stellar astrophysics and supplemented by cosmology beyond the title of the work.

A new approach in this work is the large proportion of visual materials, graphs, and video clips, contrasted with the brevity of the accompanying text. Such a form of presenting knowledge in this field is unprecedented in Slovakia, and therefore this work can be considered a completely innovative piece. It should be emphasized that the engaging form of the presented knowledge does not come at the expense of its content. The work contains all the necessary information that a physics student, especially one with a pedagogical focus, should master. The work can also be an invaluable aid to teachers in secondary and even primary schools, as well as professional astronomers in popularizing astronomical knowledge.

This suggests that the work covers a relatively wide range of needs at various institutions dealing with astronomy, from universities, through faculties of education and grammar schools, to observatories, planetariums, and astronomy clubs.

Download the e-book for free (pdf)

E-book

Ondrej Krídlo

University textbooks present the basics of knowledge systems, which are divided into two parts. The first part of the publication is devoted to the basis of Formal Concept Analysis, ie the method of data analysis, knowledge representation and information processing, which is based on the formalization of the concept. In the second part we deal with the basics of logic programming, procedural semantics of logic programming, ie programs - theories, questions, SLD-derivation, SLD-tree, search strategies.

University textbooks are intended for students of master's degree programs in computer science.

Download e-book for free (pdf)

E-book

Monika Tvrdoňová - Miroslava Martinková

The scientific book of abstracts from conference „Novel Trends in Chemistry, Research and Education 2022“ is a summary of the contributions of conference participants, which contain the original results of their scientific and research activities. The contributions published in this volume can be divided according to content into the field of analytical, inorganic, organic, physical chemistry, biochemistry, didactics of chemistry and NMR spectroscopy.

Download e-book for free (pdf)

E-book

Mária Vilková - Monika Garberová - Michal Goga

Nuclear Magnetic Resonance (NMR) is currently a widely used analytical tool that finds application in many fields of science and technology. The broadening of its practical use brings with it the necessity to create educational texts appropriate to the given scientific discipline.

This university textbook is intended for students of biology and serves as a supplement to the study materials for the advanced master's course "Biology of Lichens." At the same time, it represents a useful resource for master's and doctoral students involved in research, helping them interpret NMR spectra and present basic theoretical concepts.

The textbook briefly describes the important aspects of each NMR spectroscopic technique without delving excessively into the physical principles of individual methods or complex mathematical analyses. In this edition, the structures of lichen metabolites have been included, which students will isolate, purify, and identify using various analytical methods during practical exercises. An entire chapter is dedicated to a detailed description of solving the NMR spectra of isolated metabolites, with each step in elucidating the structures of both known and unknown metabolites explained in detail. The solved tasks are followed by numerous unsolved examples, including high-resolution 1D and 2D NMR spectra of metabolites, intended to further develop the acquired knowledge and skills of students and doctoral candidates in structure elucidation using NMR spectroscopy.

Download e-book for free (pdf)

Ondrej Hutník a kol. 

Zbierka úloh z matematickej analýzy III. je pokračovaním predchádzajúcich dvoch vydaných zbierok autorov Kulcsár a Kulcsárová. Táto časť obsahuje príklady na zopakovanie a precvičenie učiva stredných škôl, ako aj časti prvého semestra kurzu matematická analýza určeného pre študentov matematiky, fyziky, informatiky a učiteľského štúdia v kombinácii s matematikou. Zbierka môže tiež pomôcť všetkým učiteľom, ktorí chcú použiť rôzne úlohy vo svojom vyučovaní. Zbierka zahŕňa oblasť postupností reálnych čísel: aritmetické a geometrické postupnosti, všeobecne a rekurentne zadané postupnosti, nachádzajú sa tu úlohy na vyšetrovanie vlastností postupností (monotónnosť, ohraničenosť, konvergencia) a výpočet rôznych typov limít. Všetky zadané úlohy sú vyriešené na konci každej kapitoly s podrobným komentárom.

Autori

E-book

Ján Guniš - Ľubomír Šnajder

Prílohy

College scripts Programming in Python 1 are intended for future teachers of computer science. The content of the course is related to the teaching of programming in Scratch and is an introduction to text-based programming in Python.

Programming is introduced as a means of developing problem-solving skills. The first chapter is devoted to problem solving. The next 12 chapters sequentially introduce basic language constructions, data structures, and selected types of algorithms. Each of these chapters begins with an introduction to the problem. This section is primarily intended for self-study, to prepare students for the exercises. The following subchapter summarizes and completes the knowledge, and additional insights and approaches related to the chapter topic are presented. The chapters include a collection of exercises designed to practice and deepen knowledge and skills on the topic.

The final part of the chapter presents the solved problems. This section serves as a guide to solving the problems in the collection.

i

Download the e-book for free (pdf)

E-book

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.

Download the e-book for free (pdf)

E-book

Andrej Mock

The structure of the animal body is extremely varied. Each species has its distinctive morphological features, which bears as a testimony to long-term development and belonging to the developmental lineage. At the same time, the body has been tested for a long time by natural conditions, resulting in unique adaptations to the environment and life strategy. Despite this admirable variety - which includes both recent and fossil animals and which we have far from mapped – a comparison of body parts brings knowledge we can generalize: the main building principles, and boundaries within which phenotypic diversity is realized.

Comparative animal morphology today uses the latest methodological material and knowledge from other disciplines, from genetics, molecular biology and experimental embryology, through progressive imaging methods (e.g. electron microscopy, computer micro-tomography) and the possibilities of subsequent software processing of image material (measurement, staining, etc.) to the view of physics, chemistry, statics and geometry on the structures (to nanostructures) of the living body. Detailed knowledge of historical and contemporary conditions on Earth is an important interpretative context in the study of animal morphology. Surprisingly, the knowledge accumulated after centuries of research is now rapidly supplemented by new knowledge, and often the traditional knowledge is subsequently reinterpreted. Finally, and no less important, in studying animal (and human) morphology, we learn surprising knowledge about ourselves.

The author of the presented textbook had the ambition in a simplified form to introduce the reader, especially the student of biological studies, into a dynamic and fascinating scientific discipline, as the current comparative animal morphology is.

Stiahnite si e-knihu zadarmo (pdf)

E-book

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.

Download the e-book for free (pdf)