Extending the Algebraic Manipulability of Differentials
Bartlett, Jonathan and Asatur Zh. Khurshudyan. 2019. Extending the Algebraic Manipulability of Differentials. Dynamics of Continuous, Discrete and Impulsive Systems, Series A 26(3):217-230.
8 Pages Posted: 5 Oct 2019 Last revised: 23 Oct 2019
Date Written: October 22, 2019
Treating differentials as independent algebraic units have a long history of use and abuse. It is generally considered problematic to treat the derivative as a fraction of differentials rather than as a holistic unit acting as a limit, though for practical reasons it is often done for the first derivative. However, using a revised notation for the second and higher derivatives will allow for the ability to treat differentials as independent units for a much larger number of cases.
Keywords: Differentials; Inverse Function Theorem; Fa`a di Bruno; Higher-Order; Derivative; Quotient Rule
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