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1
Content available Using elements of integral calculus in the process of optimising the configuration of navigation positioning systems
Czaplewski K., Świerczyński S., Zwolan P.
Zeszyty Naukowe Akademii Morskiej w Szczecinie
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2016
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nr 45 (117)
37--43
EN
This paper presents the authors’ reflections on using integral calculus when preparing the process of locating single ground-based chains of positioning systems in marine navigation. These reflections are purely theoretical and presented research results apply to a hypothetical navigation system that operates based on the ratio of distances, which is regarded as a navigation parameter.
2
Content available Some remarks on fluid flow in hourglasses
Bryll A., Sochacki R.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2014
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Vol. 19
29--36
EN
In the paper the authors analyse different shapes of an hourglass for the linearity of their graduation. We also assume that any hourglass (more precisely, each of the two congruent parts) has the shape of a solid of revolution and any cross section at height h of this hourglass depends on the base radius r, i.e. h = ƒ(r).
3
Content available The rôle of categorical structures in infinitesimal calculus
Steingartner W., Galinec D.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 1
107--119
EN
The development of mathematics stands as one of the most important achievements of humanity, and the development of the calculus, differential calculus and integral calculus is one of the most important achievements in mathematics. Differential calculus is about finding the slope of a tangent to the graph of a function, or equivalently, differential calculus is about finding the rate of change of one quantity with respect to another quantity. On the other hand, integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Integrals and derivatives became the basic tools of calculus, with numerous applications in science and engineering. The category theory is a mathematical approach to the study of algebraic structure that has become an important tool in theoretical computing science, particularly for semantics-based research. The notion of a limit in category theory generalizes various types of universal constructions that occur in diverse areas of mathematics. In our paper we illustrate how to represent some parts of infinitesimal calculus in categorical structures.
DE
Die Theorie von Kategorien ist der Bereich von Mathematik und sie dient vor allem fur das Studium der algebraischen Strukturen. Sie wird aber sehr oft auch in Informatik geltend gemacht. Manche bedeutende mathematische Bereiche kann man mithilfe der Kategorien darstellen und das ermöglicht mit den mathematischen Strukturen viel einfacher zu arbeiten als ohne Anwendung der Kategorien. Der Grund der Infinitesimalrechnung bilden zwei duale Bereiche - Differential- und Integralrechnung. In unserem Beitrag orientieren wir uns auf die Konstruktion des Diagramms von Stammfunktionen zur Funktion Kosinus. Von diesen Funktionen konstruieren wir den kommutativen Kegel und wir finden seinen Grenzwert. In dem zweiten Teil des Artikels zeigen wir den Ausdruck der Derivationen von Funktionen in der Kommakategorie und wir konstruieren den kodomänen Funktor zwischen der Kategorie der Derivationen und der Kategorie der Mengen für differenzierbare Funktionen.
4
Content available Derivative of a function at a point and integral by professor Igor Kluvánek
Gunčaga J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2009
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Vol. 14
37-50
EN
Professor Igor Kluvánek had developed a unique course of calculus (mathematical analysis) to teach students the differential and integral calculus. In the present paper, this concept is briefly outlined. The notion of derivative is introduced via continuity. The definition of integral given in this article applies an idea of Archimedes.
5
Content available remote On mistakes connected with differentiating
Sochacki R., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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Vol. 12
399-405
EN
Many students have problems with solving tasks concerning the existence of the derivative of a function at a point. In this paper we discuss some of them.
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