Displacement Calculus

In this work, we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on to differentiation and integration. We find interesting no...

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Bibliographic Details
Published in:Mathematics (Basel) 2020-03, Vol.8 (3), p.419
Main Authors: Márquez Albés, Ignacio, Tojo, F. Adrián F.
Format: Article
Language:English
Subjects:
displacement
fundamental theorem of calculus
ordinary differential equation
stieltjes differentiation
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Summary:In this work, we establish a theory of Calculus based on the new concept of displacement. We develop all the concepts and results necessary to go from the definition to differential equations, starting with topology and measure and moving on to differentiation and integration. We find interesting notions on the way, such as the integral with respect to a path of measures or the displacement derivative. We relate both of these two concepts by a Fundamental Theorem of Calculus. Finally, we develop the necessary framework in order to study displacement equations by relating them to Stieltjes differential equations.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8030419