Zbierka úloh z matematiky pre nematematické odbory

E-book

Jozef Strečka

Over the past fifteen years, the course on ’Exactly Solvable Models in Statistical Physics’ has become an indispensable ground of the study programme ’Theoretical Physics’ at Faculty of Science of Pavol Jozef Šafarik University in Košice. At first, the course based on the first edition of this textbook was intended for undergraduate students only, however, I have later prepared follow-up course taught at a postgraduate level on demand of several ambitious students who wished to continue in studying this exciting research field.

It is already more than decade when our students enrolled in the study programme ’Theoretical Physics’ graduate from ’Introduction to Exactly Solvable Models in Statistical Physics’ at a master level and ’Exactly Solvable Models in Statistical Physics’ at a postgraduate level. Of course, it was necessary somehow to rearrange topics for the courses of undergraduate and postgraduate students.

More specifically, a few more challenging topics concerned with exact solutions of 2D Ising model (chapter 3) were moved to a more advanced course intended for the postgraduate students, while an introductory course intended for the undergraduate students was contrarily supplemented with a few new topics requiring the second edition of this textbook.

The second edition of this textbook thus contains a completely new chapter 4 devoted to the exact solution of the Ising model on the Bethe lattice using the method of exact recursion relations, while the chapter 5 was supplemented by exact results for ground state of a few frustrated Heisenberg spin models using the variational method. It is my hope that the next edition of this textbook will come soon and it will involve all topics specifically taught within the postgraduate course as well. 

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Ivan Potočňák

The script is a study literature for the subject Chemical Calculations, which is a mandatory course in the bachelor's degree programs in Chemistry and Chemistry – Interdisciplinary Studies, first year. The script contains 10 chapters with a total of 207 pages, guiding students through solved and unsolved examples to help them understand the subject matter.

Author

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Adriana Zeleňáková

One of the fundamental characteristics of the magnetic state of ferromagnetic materials is the existence of a domain structure. The university textbook "MAGNETIC DOMAINS: SPECIAL PHYSICAL PRACTICE 1" is intended primarily for students of the Master's programme in Physics of Condensed Matter FKLm and for the PhD programme in Progressive Materials PMd within the profile subject Special Practice 1 at the Institute of Physical Sciences of the Faculty of Sciences of the Pavol Jozef Šafárik University in Košice.  The textbook is divided into seven chapters. The first chapter is devoted to the basics of domain theory, including the history of domain observation and the specification of different types of energies in ferromagnetic body. The second chapter presents the relationship between domain structure and magnetisation processes in ferromagnetic materials The third chapter describes the different types of domain-wall interactions with the defect. The fourth chapter illustrates examples of domain structure in selected ferromagnetic body such as grain oriented and non-grain oriented electrical steels, amorphous and nanocrystalline ribbons. The fifth chapter summarises an overview of the different experimental methods used to visualise the domain structure and their advantages or disadvantages with respect to the structure of ferromagnetic materials. The last two chapters, the sixth and the seventh, are devoted to specific experimental tasks for observing the domain structure of a selected polycrystalline sample using the optical microscope Bitter powder method and the MFM (magnetic force microscopy) method. During the preparation of this undergraduate text, its individual parts were developed using the foreign language literature listed in the recommended references.

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Zuzana Jurašeková

Úvod k praktikám k experimentálnym metódam biofyziky

The university textbook titled Laboratory Techniques and Calculations is designed for the first-year students of the bachelor's degree in Biophysics at the Institute of Physics, Faculty of Sciences, P. J. Šafárik University in Košice. The objective is to equip students with fundamental knowledge and practical skills for the work in a chemical laboratory. It is essential for addressing different biophysical issues and experiments that students will have to solve later. The textbook comprises three principal sections: a theoretical part focused on the calculations, a section dedicated to laboratory work, and the last part offers a brief introduction to spectroscopy. The theoretical part summarizes the basic definitions and equations related to the characterization and preparation of solutions and mixtures. The second, most comprehensive part provides guidance and suggestions for safe and efficient practices in a chemical laboratory. The primary focus is on the manipulation of chemical substances and the use of specific small laboratory instruments and equipment. The fundamental laboratory procedure guides for the selected laboratory works are also provided. As part of a short introduction to spectroscopy, students can become familiar with fundamental spectroscopic concepts and principles. UV-VIS absorption spectrophotometry receives special attention, along with a brief introduction to fluorescence. The textbook is supplemented by various practical and theoretical tasks, as well as numerous web links to further explanatory texts and videos.

Download the e-book for free (pdf)

E-book

Peter Kollár

The textbook Semiconductor Elements was developed gradually over the past years as an aid for second-year master's students in condensed matter physics. It is intended to support students’ understanding of lectures, considering that important texts, mathematical relationships, and illustrations are provided in advance in the form they will be presented during the lecture.

This allows students to supplement individual pages with their own notes during the lecture, either electronically or in printed form. In this way, a study aid is created for the student, which I believe will help with the final review of knowledge gained throughout the semester in preparation for the exam. This textbook is not meant to serve as standalone literature but is designed to assist orientation in the literature, which is abundant in English but mostly written for scientists, researchers, and students for whom this topic is central and not just one of many parts of their education. Therefore, it is not allocated a larger scope in the study program.

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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]).

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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

E-book

Alena Gessert

Caves have always been very specific places throughout history. In some cultures, they served as sites for sacrifices or remembrance, while in others, they were seen as places where one could cross to the "other side of life." People used caves for shelter, as places to leave messages, to wait out bad weather, and in some cases, even lived in them. During wars in our region, entire families or villages would hide from enemies in caves, or they would use them to conceal weapons.

Today, in most countries, caves are destinations for tourists who want to experience something new and unknown: darkness, high humidity, and the fascinating beauty of underground formations. They are also sought after by cavers who long to explore caves, enter worlds where no human has set foot before, find evidence of previous habitation, or conduct research that continually advances our knowledge.

In the publication you are holding, we present both traditional and less conventional topics about the formation of karst and caves, selected ecological aspects, maps and their creation, significant caves of the world, and the life of people in such areas. We also offer an overview of important karst locations that are definitely worth learning more about or visiting in person. This publication is intended for readers among pupils, students, teachers, and the general public, and we believe it will draw you into this mysterious world.

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Renáta Oriňáková (ed.)

Book of abstract

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Katarína Cechlárová

Linear programming belongs to parts of mathematics with the greatest number of real applications. This Slovak-English problem collection provides an overview of basic knowledge in the area, application problems as well as problems to acquire routine in calculations. It is complemented by questions motivating the student to look for further theoretical principles, construct conterexamples  and formulate arguments to explain the studied phenomena.

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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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Pavol Sokol - Ladislav Bačo - Tomáš Bajtoš

In the university textbook, we present the theoretical foundations and technical details of the activities of a forensic investigator. We describe the identification and provision of digital tracks, file system analysis. analysis of various artifacts of the Windows operating system, analysis of the operating memory. The textbook is also supplemented by a chapter devoted to the analysis of malicious code (malware). University textbooks are intended for students of bachelor's, master's, engineering and doctoral study programs in computer science, but also in non-informatics fields.

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Erik Sedlák - Rastislav Varhač -  Patrik Danko - Helena Paulíková - Dušan Podhradský

The presented scripts were created in an effort to update and especially clarify the tasks that are solved in the basic practical exercises in biochemistry students of the 2nd and 3rd year of the bachelor's degree in chemistry, biology and their combinations with other disciplines. Most of the tasks come from the original scripts "Podhradský, Mihalovová: Praktické cvičenia z biochémie, Košice 1989".

Some of them have been modified to a greater or lesser extent and adapted to current conditions in the laboratory. New tasks were also added, such as those dedicated to nucleic acids. The scripts are thematically divided into six separate units, each of which consists of several tasks. The names of the units correspond to the nature of the biomacromolecules, which form their central theme. Theoretical introductions at the beginning of the unit are newly constructed and their main goal is to provide a brief overview of the basic biochemical methods used in the study of biomacromolecules.

These scripts are intentionally only available in electronic form. The reason is the effort to continuously update and modernize individual tasks according to the changing possibilities of our laboratory. We hope that the scripts will fulfill their role and that students will have sufficient theoretical knowledge and practical skills in the field of basic biochemical methods after completing these laboratory exercises.

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Vladimír Zeleňák (ed.)

The publication contains abstracts of contributions presented at the Student Scientific Conference of the Faculty of Natural Sciences at UPJŠ in Košice, held on April 25, 2013. The event was marked by the celebration of the 50th anniversary of the Faculty of Natural Sciences at UPJŠ and was part of a series of events called ScienceFest.

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Jana Shepa - Ivana Šišoláková (eds.)

Abstracts of the 4th International Conference Nanomaterials: Fundamentals and Applications (NFA) 2020 is the contributions summary of the conference participants. The conference will feature three invited lectures and eight registered lectures. This conference is a tool for creating a dialogue between experts in the field of nanomaterials, their use and overall application in various fields. Papers in the proceedings are thematically divided into 6 areas. All contributions are highly professional and interesting and can contribute to further creative scientific work.

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Michal Hnatič - Tomáš Lučivjanský

This textbook is primarily intended for first-year master's degree students at Pavol Jozef Šafárik University in Košice, especially those in the nuclear physics, subnuclear physics, and theoretical physics programs. For many years, these lectures were taught by one of the authors at this university, and naturally, over time, there arose an effort to provide these lectures to students in printed form.

In this textbook, we will focus mainly on classical field theory, its quantization based on the operator approach, and the introduction of interactions. Descriptions based on functional integration, Feynman diagram techniques, and more advanced parts will be covered in a subsequent volume of the textbook. In this context, we want to emphasize that in many modern quantum field theory textbooks, the operator approach is used to a lesser extent and is replaced by the approach using (functional) path integrals.

This is probably due to time considerations, as the functional approach leads much faster to practical calculations. On the other hand, we believe that the operator approach is better from a pedagogical point of view. It is much closer to the traditional quantum mechanics course, which is often based on the Schrödinger or Heisenberg formalism. Therefore, students can much more easily follow the flow of ideas that led to the construction of quantum field theory and its fundamental concepts.

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E-book

Jozef Strečka

Over the past fifteen years, the course on ’Exactly Solvable Models in Statistical Physics’ has become an indispensable ground of the study programme ’Theoretical Physics’ at Faculty of Science of Pavol Jozef Šafarik University in Košice. At first, the course based on the first edition of this textbook was intended for undergraduate students only, however, I have later prepared follow-up course taught at a postgraduate level on demand of several ambitious students who wished to continue in studying this exciting research field.

It is already more than decade when our students enrolled in the study programme ’Theoretical Physics’ graduate from ’Introduction to Exactly Solvable Models in Statistical Physics’ at a master level and ’Exactly Solvable Models in Statistical Physics’ at a postgraduate level. Of course, it was necessary somehow to rearrange topics for the courses of undergraduate and postgraduate students.

More specifically, a few more challenging topics concerned with exact solutions of 2D Ising model (chapter 3) were moved to a more advanced course intended for the postgraduate students, while an introductory course intended for the undergraduate students was contrarily supplemented with a few new topics requiring the second edition of this textbook.

The second edition of this textbook thus contains a completely new chapter 4 devoted to the exact solution of the Ising model on the Bethe lattice using the method of exact recursion relations, while the chapter 5 was supplemented by exact results for ground state of a few frustrated Heisenberg spin models using the variational method. It is my hope that the next edition of this textbook will come soon and it will involve all topics specifically taught within the postgraduate course as well. 

Download the e-book for free  (pdf)

E-book

Ivan Potočňák

The script is a study literature for the subject Chemical Calculations, which is a mandatory course in the bachelor's degree programs in Chemistry and Chemistry – Interdisciplinary Studies, first year. The script contains 10 chapters with a total of 207 pages, guiding students through solved and unsolved examples to help them understand the subject matter.

Author

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E-book

Adriana Zeleňáková

One of the fundamental characteristics of the magnetic state of ferromagnetic materials is the existence of a domain structure. The university textbook "MAGNETIC DOMAINS: SPECIAL PHYSICAL PRACTICE 1" is intended primarily for students of the Master's programme in Physics of Condensed Matter FKLm and for the PhD programme in Progressive Materials PMd within the profile subject Special Practice 1 at the Institute of Physical Sciences of the Faculty of Sciences of the Pavol Jozef Šafárik University in Košice.  The textbook is divided into seven chapters. The first chapter is devoted to the basics of domain theory, including the history of domain observation and the specification of different types of energies in ferromagnetic body. The second chapter presents the relationship between domain structure and magnetisation processes in ferromagnetic materials The third chapter describes the different types of domain-wall interactions with the defect. The fourth chapter illustrates examples of domain structure in selected ferromagnetic body such as grain oriented and non-grain oriented electrical steels, amorphous and nanocrystalline ribbons. The fifth chapter summarises an overview of the different experimental methods used to visualise the domain structure and their advantages or disadvantages with respect to the structure of ferromagnetic materials. The last two chapters, the sixth and the seventh, are devoted to specific experimental tasks for observing the domain structure of a selected polycrystalline sample using the optical microscope Bitter powder method and the MFM (magnetic force microscopy) method. During the preparation of this undergraduate text, its individual parts were developed using the foreign language literature listed in the recommended references.

Download the e-book for free (pdf)

E-book

Zuzana Jurašeková

Úvod k praktikám k experimentálnym metódam biofyziky

The university textbook titled Laboratory Techniques and Calculations is designed for the first-year students of the bachelor's degree in Biophysics at the Institute of Physics, Faculty of Sciences, P. J. Šafárik University in Košice. The objective is to equip students with fundamental knowledge and practical skills for the work in a chemical laboratory. It is essential for addressing different biophysical issues and experiments that students will have to solve later. The textbook comprises three principal sections: a theoretical part focused on the calculations, a section dedicated to laboratory work, and the last part offers a brief introduction to spectroscopy. The theoretical part summarizes the basic definitions and equations related to the characterization and preparation of solutions and mixtures. The second, most comprehensive part provides guidance and suggestions for safe and efficient practices in a chemical laboratory. The primary focus is on the manipulation of chemical substances and the use of specific small laboratory instruments and equipment. The fundamental laboratory procedure guides for the selected laboratory works are also provided. As part of a short introduction to spectroscopy, students can become familiar with fundamental spectroscopic concepts and principles. UV-VIS absorption spectrophotometry receives special attention, along with a brief introduction to fluorescence. The textbook is supplemented by various practical and theoretical tasks, as well as numerous web links to further explanatory texts and videos.

Download the e-book for free (pdf)

E-book

Peter Kollár

The textbook Semiconductor Elements was developed gradually over the past years as an aid for second-year master's students in condensed matter physics. It is intended to support students’ understanding of lectures, considering that important texts, mathematical relationships, and illustrations are provided in advance in the form they will be presented during the lecture.

This allows students to supplement individual pages with their own notes during the lecture, either electronically or in printed form. In this way, a study aid is created for the student, which I believe will help with the final review of knowledge gained throughout the semester in preparation for the exam. This textbook is not meant to serve as standalone literature but is designed to assist orientation in the literature, which is abundant in English but mostly written for scientists, researchers, and students for whom this topic is central and not just one of many parts of their education. Therefore, it is not allocated a larger scope in the study program.

Download e-book for free (pdf)