Skenovacia tunelová mikroskopia

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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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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.

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Jozef Kováčik

These "Exercise Manuals" present a concise overview of commonly used methodologies as well as progressive techniques, such as the use of liquid chromatography and fluorescence microscopy. Individual tasks were selected based on the research focus of the Department of Botany at the Faculty of Science, Pavol Jozef Šafárik University in Košice, particularly in the context of "stress physiology."

Some tasks can also be utilized within the subject "Plant Ecology." Chamomile (Matricaria chamomilla) is typically used as a model plant for individual tasks due to its long-standing history of research at the Department of Botany and its ease of cultivation under laboratory conditions. The chapters also briefly discuss the significance of monitored parameters, principles of their determination, and metabolism (formation or degradation), aiming to indicate their mutual context.

This approach highlights that determining an individual parameter cannot provide a general explanation for the overall causes and impacts of observed changes; however, it can serve as a basis for testing hypotheses at the level of other parameters.

For deeper study of specific issues, there is an abundance of high-quality international monographs and review articles available.

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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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Ľubomír Kováč

Učebný text „Zoogeografia“ objasňuje základné princípy a historický vývoj rozšírenia živočíchov na Zemi, a ďalej analyzuje faktory, ktoré ho ovplyvňujú. Vďaka moderným vedeckým metódam a technikám výskumu je zoogeografia veľmi dynamicky sa rozvíjajúcou disciplínou. Z geologických etáp je podrobnejšie spracovaná problematika paleoklimatických cyklov kvartéru, holocénu a vývoja postglaciálnej klímy, ktoré zohrali významnú úlohu pri dynamike vývoja živočíšnych areálov. Areálová analýza charakterizuje a triedi areály živočíchov a ich dynamiku v nadväznosti na speciáciu. Podrobne je spracovaná problematika zoogeografických oblastí s dôrazom na palearktickú oblasť. Časť zameraná na dynamickú zoogeografiu rieši najmä problematiku refúgií a reliktov v súvislosti s vývojom pleistocénnej paleoklímy. Text stručnou formou sumarizuje základné antropogénne faktory, ktoré v recentnej dobe drastickým spôsobom limitujú rozšírenie živočíchov v rýchlo ubúdajúcom prírodnom prostredí na Zemi. Text ďalej prehľadným spôsobom charakterizuje biogeografiu Karpát a faunu územia Slovenska. Záverečná časť prezentuje fylogeografiu ako modernú vednú disciplínu zameranú na rekonštrukciu migračných ciest v postglaciáli, ktorá je podložená analýzou molekulárnych markerov populácií živočíchov v širšom geografickom kontexte. 

Autor

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Juraj Ševc - Filip Mochnacký

Students studying biology as the single-subject or as a part of two-subject programs on various faculties of sciences are often encountered with the problem, how to limit the topics in the subject Human anatomy. This List of anatomical terms is aiming to help the non-medical students to get acquainted with the extensive anatomical nomenclature and to optimize the number of anatomical terms, which should be memorized, to preserve the sufficient capacity of the students for another knowledge of the field of systemic, comparative, developmental and functional anatomy. The emphasis on the arrangement of individual anatomical terms into the logical units supports the hierarchical view on the architecture of the human body.

Despite the common opinion, anatomical nomenclature represents a framework, which is during the further study gradually enveloped with the knowledge of more or less related disciplines concerning with the human body and its biological processes. Moreover, besides this ambition, which exceeds the area of the human anatomy, this List of anatomical terms continues the long tradition with respect to the valid Latin and Slovak anatomical terminology.

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Danica Sabolová

This university textbook is intended for students of the Faculty of Science of the University of Applied Sciences in Košice who have enrolled in practical exercises in Biotechnology, but also for all other students who are interested in learning about the practical applications of biotechnology.

The aim of the practical course is to familiarize students with basic biotechnological methods and their applications. The students will verify in practice the theoretical knowledge acquired in the Biotechnology lectures such as the course of fermentation processes, wine production, preparation of fermented milk products and cheese, preparation of culture media, inoculation and cultivation of microorganisms, etc. The practical exercises also include the use of analytical and spectral methods, which are an integral part of biochemistry.

The scripts are published only in electronic form and are available on the University's website: http://kosice.upjs.sk/~kbch/sk, for the reason that it will always be possible to update and modernize the content of the laboratory exercises.

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Miroslav Almáši  Nikolas Király   eds.

The conference proceedings of Porous Materials for Environmental Applications 2026 represent a collection of scientific and professional contributions presented at the international scientific conference held on 15–19 March 2026 in Białka Tatrzańska (Poland). The conference focused on current trends in the research of porous materials and their applications in environmental, catalytic, energy-related, and biomedical fields. The event provided an interdisciplinary platform for the exchange of the latest scientific knowledge in the design, synthesis, characterization, and practical utilization of porous materials.

Particular attention was devoted to their application in adsorption and separation processes, heterogeneous catalysis, photocatalysis, energy storage and conversion, as well as in biological and medical applications. The published abstracts reflect current challenges related to sustainable development, green technologies, and advanced materials solutions. The proceedings offer a comprehensive overview of the current state of porous materials research at the international level and document the dynamic development of this field with significant overlap into environmental chemistry, materials science, and chemical engineering.

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Peter Paľove-Balang

The text ‘Uptake and transport of mineral substances in plants’ in Slovak language provides a general overview of the uptake and distribution of substances in an easy-to-understand form.

The individual chapters introduce students to the properties of the soil environment, which have a significant influence on the availability of substances, as well as the transport of substances across membranes and over medium and long distances. The text contains the latest findings from the English literature, supplemented by diagrams and graphs created by the author on the basis of his own research or by compiling several sources.

The text is intended primarily for students of a master's degree in biology or ecology and assumes at least a basic knowledge of plant physiology.

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Michal Jaščur -Michal Hnatič

In the textbook, the processes belonging to an area of  nonequilibrium physics, which make the basis for the study and analysis of compex phenomena  of statistical mechanics, are described. The Boltzmann equation for distribution function is derived and on this basis the hydrodynamic equations are constructed.  Stochastic processes are described separately and Fokker-Planck equation for density probability  is derived. Textbook is intended for the students of second year of master study at Faculty of Science of P. J. Šafarik University.   

Autors

Igor Hudec - Ľubomír Kováč 

The study course provides the basic knowledge on the fundamental parameters, relationships and processes in ecological sciences. Brief content: ecological factors and relations to environment (air, water, soil); influence of ecological factors upon organisms (morphological adaptations, behavioural responses); populations and communities (external and internal parameters of populations, population dynamics); ecosystems (impact assessment) and biomes (basic features and human impact); cycles (hydrologic, gaseous, sedimentation) of basic elements on Earth.  

Authors

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Vladimír Zeleňák (ed.)

The proceedings contain contributions from participants of the Student Scientific Conference of the Faculty of Science at UPJŠ in Košice, which took place on April 24, 2014.

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Janetta Nestorová Dická

The university handbook Elementals of Population Geography and Demography - Part I, as an introduction to population studies, is primary study material for students of the geography study program, as well as for students of the Information Systems in Public Administration study program at the Pavel Jozef Šafárik University in Košice, but also for the wider public interested in about population phenomena and their spatiality. Among other things, the handbook offers the latest population reports in the world and its regions.

The aim of the handbook is to introduce young geographers to the basics of population research, which includes the most frequently used tools and methods in geographic analysis. The first part of the handbook contains an introduction to the scientific disciplines of population geography and demography with an overview of basic sources of demographic data.

The next part discusses the issue of anthropogenesis, i.e. the development of humans from our ancestors and the spatial spread of humans across our Earth. Part of this part is the recent development of the world population and changes in the size and distribution of the global population over time. The last part analyses how the population is distributed in the world and in relation to the geographical components of the space.

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Marek Bombara

The collection of exercises summarises and supplements the exercises realised at the Pavol Jozef Šafárik in Košice within the lecture course Elementary Particle Physics. The collection is intended for the master students of the Nuclear and Subnuclear Physics subject, but it could be beneficial also for other physics subjects or even for interdisciplinary study. 

The division of chapters roughly copies the order of lectures. At the beginning, students will briefly familiarize themselves with the basics of special relativity and its practical use in particle physics.

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Janka Vrláková - Stanislav Vokál

Atomic and nuclear physics are relatively young scientific disciplines forming the final part of the general physics course at the Faculty of Physics of the Jagiellonian University. Their aim is to explain the nature of the basic physical properties of atoms, atomic nucleus and elementary particles.

This is also the content of the lectures and exercises ‘General Physics IV’ in the 2nd year of the Bachelor's degree in Physics at the Faculty of Natural Sciences (PF) of the P.J. Šafárik University (UPJŠ) in Košice. They are followed by optional lectures ‘Nuclear Radiation in the Environment’, ‘Introduction to the Physics of the Microworld’ in the 3rd year of the Bachelor's degree of single-discipline study of physics, or teacher study of physics in combination with another subject, and ‘Subnuclear Physics’ in the 1st year of the Master's degree of teacher study of physics in combination with another subject.

In the aforementioned lectures, the latest experimental findings on the structure and behaviour of the microworld are presented by means of physical theories and their subsequent experimental verification in experiments.

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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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