Displacement Calculus
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http://hdl.handle.net/10347/23643
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| Title: | Displacement Calculus |
| Author: | Márquez Albés, Ignacio Fernández Tojo, Fernando Adrián |
| Affiliation: | Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización |
| Subject: | Displacement | Ordinary differential equation | Fundamental theorem of calculus | Stieltjes differentiation | |
| Date of Issue: | 2020 |
| Publisher: | MDPI |
| Citation: | Márquez Albés, I.; Tojo, F.A.F. Displacement Calculus. Mathematics 2020, 8, 419 |
| Abstract: | 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 |
| Publisher version: | https://doi.org/10.3390/math8030419 |
| URI: | http://hdl.handle.net/10347/23643 |
| DOI: | 10.3390/math8030419 |
| E-ISSN: | 2227-7390 |
| Rights: | © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) Atribución 4.0 Internacional |
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Except where otherwise noted, this item's license is described as © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)