Outline of the introduction to the natural differential and integral calculus.
Φόρτωση...
Ημερομηνία
Συγγραφείς
Kyritsis, Konstantinos E.
Τίτλος Εφημερίδας
Περιοδικό ISSN
Τίτλος τόμου
Εκδότης
University of the Aegean, Department of Geography, George Korres.
Περίληψη
Τύπος
Είδος δημοσίευσης σε συνέδριο
Είδος περιοδικού
peer-reviewed
Είδος εκπαιδευτικού υλικού
Όνομα συνεδρίου
Όνομα περιοδικού
Journal of Regional & Socio-Economic Issues.
Όνομα βιβλίου
Σειρά βιβλίου
Έκδοση βιβλίου
Συμπληρωματικός/δευτερεύων τίτλος
Outline of the introduction to the natural or digital differential and integral calculus.
Περιγραφή
In this paper I go further from the digital continuous axiomatic Euclidean geometry ([8]) and introduce the basic definitions and derive the basic familiar properties of the differential and integral calculus without the use of the infinite, within finite sets only. No axioms are required in this only successfully chosen definitions. I call it the natural differential and integral calculus. Such mathematics is probably the old unfulfilled hitherto dream of the mathematicians since many centuries. Strictly speaking it is not equivalent to the classical differential and integral calculus which makes use of the infinite (countable and uncountable) and limits. Nevertheless, for all practical reasons in the physical and social sciences it gives all the well-known applications with a finite ontology which is directly realizable both in the physical ontology of atomic matter or digital ontology of operating systems of computers. Such a natural or digital calculus has aspects simpler than the classical "analogue" calculus which often has a complexity irrelevant to the physical reality. It can become also more complicated than the classical calculus when more than 2 resolutions are utilized, but this complexity is directly relevant to the physical reality. The natural differential and integral calculus is of great value for the applied physical and social sciences as its ontology is directly corresponding to the ontology of computers. It is also a new method of teaching mathematics where there is integrity with what we say, write, see, and think. In this short outline of the basic natural differential and integral calculus, we include on purpose almost only the basic propositions that are almost identical with the corresponding of the classical calculus for reasons of familiarity with their proofs.
Περιγραφή
Λέξεις-κλειδιά
Digital mathematics, Calculus
Θεματική κατηγορία
Mathematics
Παραπομπή
Σύνδεσμος
Γλώσσα
en
Εκδίδον τμήμα/τομέας
Όνομα επιβλέποντος
Εξεταστική επιτροπή
Γενική Περιγραφή / Σχόλια
Ίδρυμα και Σχολή/Τμήμα του υποβάλλοντος
University of Iannina, School of Economic and Administrative Sciences, Dept of Accouning-Finance
Πίνακας περιεχομένων
Χορηγός
Βιβλιογραφική αναφορά
Kyritsis, K. (2019). Outline of the introduction to the natural differential and integral calculus. Journal of Regional & Socio-Economic . Vol. 9, Issue 3, p.p.70-89.
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Αριθμός σελίδων
Λεπτομέρειες μαθήματος
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Άδεια Creative Commons
Άδεια χρήσης της εγγραφής: Attribution-NonCommercial-NoDerivs 3.0 United States