Displacement Calculus
In this work, we establish a theory of Calculus based on the new concept of <i>displacement</i>. 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...
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Format: | Article |
Language: | English |
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MDPI AG
2020-03-01
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Series: | Mathematics |
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Online Access: | https://www.mdpi.com/2227-7390/8/3/419 |
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author | Ignacio Márquez Albés F. Adrián F. Tojo |
author_facet | Ignacio Márquez Albés F. Adrián F. Tojo |
author_sort | Ignacio Márquez Albés |
collection | DOAJ |
description | In this work, we establish a theory of Calculus based on the new concept of <i>displacement</i>. 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. |
first_indexed | 2024-12-11T12:05:30Z |
format | Article |
id | doaj.art-d223366d377f416f8d8cb14f557114f8 |
institution | Directory Open Access Journal |
issn | 2227-7390 |
language | English |
last_indexed | 2024-12-11T12:05:30Z |
publishDate | 2020-03-01 |
publisher | MDPI AG |
record_format | Article |
series | Mathematics |
spelling | doaj.art-d223366d377f416f8d8cb14f557114f82022-12-22T01:07:57ZengMDPI AGMathematics2227-73902020-03-018341910.3390/math8030419math8030419Displacement CalculusIgnacio Márquez Albés0F. Adrián F. Tojo1Instituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, SpainInstituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, SpainIn this work, we establish a theory of Calculus based on the new concept of <i>displacement</i>. 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.https://www.mdpi.com/2227-7390/8/3/419displacementordinary differential equationfundamental theorem of calculusstieltjes differentiation |
spellingShingle | Ignacio Márquez Albés F. Adrián F. Tojo Displacement Calculus Mathematics displacement ordinary differential equation fundamental theorem of calculus stieltjes differentiation |
title | Displacement Calculus |
title_full | Displacement Calculus |
title_fullStr | Displacement Calculus |
title_full_unstemmed | Displacement Calculus |
title_short | Displacement Calculus |
title_sort | displacement calculus |
topic | displacement ordinary differential equation fundamental theorem of calculus stieltjes differentiation |
url | https://www.mdpi.com/2227-7390/8/3/419 |
work_keys_str_mv | AT ignaciomarquezalbes displacementcalculus AT fadrianftojo displacementcalculus |