Displacement Calculus

Ignacio Márquez Albés and F. Adrián F. Tojo
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Ignacio Márquez Albés: Instituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, Spain
F. Adrián F. Tojo: Instituto de Matemáticas, Universidade de Santiago de Compostela, 15705 Santiago de Compostela, Spain

Mathematics, 2020, vol. 8, issue 3, 1-30

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.

Keywords: displacement; ordinary differential equation; fundamental theorem of calculus; Stieltjes differentiation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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