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Displacement Calculus

Instituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, Spain
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Mathematics 2020, 8(3), 419; https://doi.org/10.3390/math8030419
Received: 4 January 2020 / Revised: 24 February 2020 / Accepted: 8 March 2020 / Published: 14 March 2020
(This article belongs to the Section Difference and Differential Equations)
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. View Full-Text
Keywords: displacement; ordinary differential equation; fundamental theorem of calculus; Stieltjes differentiation displacement; ordinary differential equation; fundamental theorem of calculus; Stieltjes differentiation
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Márquez Albés, I.; Tojo, F.A.F. Displacement Calculus. Mathematics 2020, 8, 419.

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