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

See all articles by Jonathan Bartlett

Jonathan Bartlett

ITX Corp; The Blyth Institute; Bradley Center for Natural and Artificial Intelligence

Asatur Khurshudyan

National Academy of Sciences of Armenia

Date Written: October 22, 2019

Abstract

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

Suggested Citation

Bartlett, Jonathan and Khurshudyan, Asatur, Extending the Algebraic Manipulability of Differentials (October 22, 2019). 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.. Available at SSRN: https://ssrn.com/abstract=3459227

Jonathan Bartlett (Contact Author)

ITX Corp ( email )

1169 Pittsford-Victor Road
Suite 100
Pittsford, NY 14534
United States

The Blyth Institute ( email )

8835 S Kingston Ave
Tulsa, OK 74137
United States

Bradley Center for Natural and Artificial Intelligence ( email )

208 Columbia Street
Seattle, WA 98104
United States

Asatur Khurshudyan

National Academy of Sciences of Armenia

Armenia

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