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arXiv:1801.09553math.GM

Extending the Algebraic Manipulability of Differentials

Jonathan Bartlett, Asatur Zh. Khurshudyan

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.

arXiv comments
8 pages
Journal reference
Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis 26(3):217-230, 2019
DOI
Subjects
math.GMGeneral Mathematics

On Hacker News

Linked by 6 identifiable commenters in 7 comments across 6 threads, from Jul 2019 to Jan 2025. Found in 4 HN submissions from Nov 2018 to Nov 2024. Open submission discussions.

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Discussed in comments6 threads

  1. Multiplicative Infinitesimals 1 comment

    • If you are going to use infinitesimals, though, it requires some additional doing for notation. The standard notation for higher-order derivatives (and partial derivatives) needs to be modified in order for them to work (but they do work great once you do this). Instead of the…

      johnnyb_61820View on HNParent context

  2. On Leibniz Notation 2 comments

    • A somewhat relevant article, it explores an alternative to Leibniz notation: Extending the Algebraic Manipulability of Differentials (https://arxiv.org/pdf/1801.09553.pdf).

      LudwigNagasenaView on HNParent context

    • I've learned calculus a few times in and out of school. I learned it best from a home-schooling focused text book. The author published a paper describing his notation [0]; see section 3 which is very readable. The paper explains: > Most calculus students glaze over the notation…

      Buttons840View on HNParent context

  3. Notation for Differentiation 1 comment

    • There is a really good paper on better notations for differentiation https://arxiv.org/abs/1801.09553 in such a way that algebraic manipulations of the "dx" etc have meaning. The main proposition is to stop calling the second derivative of y along x d^2y/(dx)^2 since this is…

      lapinotView on HNParent context

  4. Correctness and composability bugs in the Julia ecosystem 1 comment

    • Math traditionally has had some bad notation from a formal point of view, because humans are good at coping with bad notations (or going back and forth between variants), unlike machines and formal systems. Computer science being a (more) formal science (vs math which is…

      lapinotView on HNParent context

  5. Tulsa Teacher discovers calculus flaw 1 comment
  6. Calculus for Beginners and Artists (2003) 1 comment

    • Check out Bartlett’s papers and textbook if you want something based on differentials, https://arxiv.org/abs/1811.03459 https://arxiv.org/abs/1801.09553 https://amzn.com/1944918027

      jacobolusView on HNParent context

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