Určitý integrál

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)

Quantity

978-80-7097-929-7

Data sheet

Method of publication:
E-book (pdf)
Author:
Ondrej Hutník
Document type:
Academic textbook - scripts
Number of pages:
91
Available from:
15.01.2012
Year of publication:
2012
Edition:
1st edition
Publication language:
Slovak
Faculty:
Prírodovedecká fakulta
- Free for download

16 other products in the same category:

Praktikum z nukleárnej magnetickej rezonancie....

E-book

E-book

Mária Vilková - Zuzana Kudličková - Aneta Salayová - Tomáš Ján Liška

The Nuclear Magnetic Resonance Practicum – Part 1: Quantitative NMR is designed for students taking the NMR Practicals course, which focuses on the practical aspects of quantitative nuclear magnetic resonance (qNMR). This publication builds on previous NMR courses and assumes basic theoretical knowledge of the method, emphasizing experimental procedures, data processing, and result interpretation. qNMR is a precise analytical technique with broad applications in analytical chemistry, pharmaceutical research, biomedicine, and quality control. The script provides a detailed guide to conducting experiments, as well as procedures for analyzing and evaluating acquired data. This publication offers students methodological guidance and support in mastering qNMR analysis and serves as a valuable resource not only during their studies but also for further research in NMR spectroscopy.

Download the e-book for free (pdf)

Autumn Electrochemical Meeting

E-book

E-book

Jana Shepa (ed.)

The book of abstracts from the first year of the international conference Autumn electrochemical meeting is composed of contributions from the participants of this student conference.

The conference consisted of one invited lecture and six student lectures. The message of this meeting is to create a dialogue between students of electrochemistry and the mutual exchange of knowledge. All contributions are professionally processed and inspiring.

Download the e-book for free  (pdf)

Praktické cvičenia z fyzikálnej chémie

E-book

E-book

Andrea Morovská TuroňováRenáta OriňakováFrantišek Kaľavský 

The university textbooks "Practical Exercises in Physical Chemistry" are intended as teaching literature for students of the 2nd year of the Chemistry study program and the 3rd year of the interdisciplinary study program at the Faculty of Science of the Pavel Jozef Šafárik University in Košice.

The three chapters summarize the basic knowledge of thermodynamics, electrochemistry and kinetics, the next chapter deals with the measurement of some other physico-chemical quantities. The tasks developed on the basis of cooperation with the Criminalistics and Expertise Institute of the Police in Košice, which also participates in the innovation of practical teaching, are also very attractive and interesting for students. Thematic units are updated and supplemented by new knowledge, principles as well as detailed working procedures using new instrumentation.

The aim of laboratory exercises in physical chemistry is to illustrate and confirm the physicochemical laws and correlations that apply to the quantitative description of chemical phenomena. Students will learn to use instruments and equipment that occur in physico-chemical laboratories, they will learn the principles of accurate and correct quantitative measurement of physical quantities, important from a chemical point of view. They can also develop professional and scientific communication skills, and we want to support their creative approach to making measurement protocols.

Download the e-book for free  (pdf)

NOVEL TRENDS IN CHEMISTRY, RESEARCH AND...

E-book

E-book

Miroslav Almáši

The scientific book of abstracts from the conference „Novel Trends in Chemistry, Research and Education 2023“ 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 fields of analytical, inorganic, organic, physical chemistry, biochemistry, didactics of chemistry, and NMR spectroscopy.

Download e-book for free (pdf)

Cognitive neuroscience of auditory and...

E-book

Norbert Kopčo - Frederick Gallun - Beáta Tomoriová - Ľuboš Hládek(eds.)

Cognitive neuroscience is a fast developing scientific field which aims at uncovering the neural basis of human perception and cognition. To achieve this goal, cognitive neuroscience uses a variety of tools and approaches ranging from non-invasive brain imaging to psychophysics and neural modeling. Mastering such tools requires skills and knowledge from multiple scientific domains, including neurophysiology, cognitive psychology, and several computational fields.

Prístup na požiadanie na email: kogneuro (@) gmail.com

http://pcl.upjs.sk/workshopcd 

https://sites.google.com/site/kogneuro/

This website uses cookies to ensure you get the best experience on our website