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.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference29 articles.
1. A Treatise of the Method of Fluxions and Infinite Series;Newton,1736
2. Absolute differentiation in metric spaces;Charatonik;Houston J. Math.,2012
3. Mutational Analysis: A Joint Framework for Cauchy Problems in and Beyond Vector Spaces;Lorenz,2010
4. A New Unification of Continuous, Discrete, and Impulsive Calculus through Stieltjes Derivatives
5. Lusin’s theorem for derivatives with respect to a continuous function
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