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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Main Authors: Ignacio Márquez Albés, F. Adrián F. Tojo
Format: Article
Language:English
Published: MDPI AG 2020-03-01
Series:Mathematics
Subjects:
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.
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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