Úvod do otvoreného prístupu

E-book

Jitka Dobbersteinová - Silvia Horáková - Simona Hudecová & Zuzana Stožická

The textbook for Module 1 of the course "Introduction to Open Access." Upon completing this module, it is expected that you will be able to understand scholarly communication and open access, advocate for various forms of open access and distinguish between them, master the issues of rights management including copyright law, copyleft as a special use of copyright, and related intellectual property rights, and explain the significance of open access in the context of scholarly communication.

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Quantity

Data sheet

Method of publication:
E-book (pdf)
Authors:
Jitka Dobbersteinová - Silvia Horáková - Simona Hudecová & Zuzana Stožická
Document type:
University Textbook
Available from:
19. apríl 2021
Year of publication:
2021
Edition:
1st edition
Publication language:
Slovak
License:
CC BY NC SA (Uveďte autora - Nepoužívajte komerčne - Zachovajte licenciu )
DOI:
https://doi.org/10.5281/zenodo.4704871

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Určitý integrál

Určitý integrál

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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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Geografické poznatky bez hraníc - výber z maďarských a slovenských príspevkov z fyzickej a humánnej geografie.

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Dušan Barabas a kol.

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