Extending the Algebraic Manipulability of Differentials · HackerPapers discussions

Extending the Algebraic Manipulability of Differentials — mentioned by johnnyb_61820

Wed, 08 Jan 2025 23:05:34 GMT

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 second derivative being "d^2y/dx^2" it is "(d^2y/dx^2) - (dy/dx)(d^2x/dx^2)" and the differentials can be manipulated just like any other entity. Additionally, you can infer this notation by simply applying the quotient rule to the first derivative (which is a quotient of infinitesimals). See more: "Extending the…

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Extending the Algebraic Manipulability of Differentials — HN submission

Fri, 08 Nov 2024 06:46:23 GMT

Extending the Algebraic Manipulability of Differentials (2018) [pdf]

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Extending the Algebraic Manipulability of Differentials — mentioned by Buttons840

Sat, 20 Jan 2024 11:45:51 GMT

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 for higher derivatives, and few, if any, books bother to give any reasons behind what the notation means. It's important to go back and consider why the notation is what it is, and what the pieces are supposed to represent. > In modern calculus, the derivative is always taken with respect to some variable. However…

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Extending the Algebraic Manipulability of Differentials — mentioned by LudwigNagasena

Sat, 20 Jan 2024 08:17:06 GMT

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

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Extending the Algebraic Manipulability of Differentials — mentioned by lapinot

Sun, 10 Jul 2022 12:16:59 GMT

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 completely wrong if you want to manipulate things algebraically. In this notation the exponent is denoting function composition and not multiplication.

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Extending the Algebraic Manipulability of Differentials — mentioned by lapinot

Mon, 16 May 2022 16:18:55 GMT

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 overwhelmingly not done formally), it has criticized some traditional math notation which are ad-hoc and not nicely formalizable (and put forward variants that are actually better behaved in terms of mathematical structures). For indices: indices are about referencing elements of finite ordered sets, say of size N. Hence the…

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Extending the Algebraic Manipulability of Differentials — HN submission

Tue, 16 Jul 2019 22:43:03 GMT

Extending the Algebraic Manipulability of Differentials

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Extending the Algebraic Manipulability of Differentials — mentioned by lyctc

Mon, 15 Jul 2019 17:57:08 GMT

"Extending the Algebraic Manipulability of Differentials" https://arxiv.org/pdf/1801.09553.pdf

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Extending the Algebraic Manipulability of Differentials — mentioned by jacobolus

Sun, 14 Jul 2019 22:58:24 GMT

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

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Extending the Algebraic Manipulability of Differentials — HN submission

Thu, 02 May 2019 16:44:13 GMT

Extending the Algebraic Manipulability of Differentials

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Extending the Algebraic Manipulability of Differentials — HN submission

Sat, 10 Nov 2018 19:23:11 GMT

Extending the Algebraic Manipulability of Differentials

17 points; 3 discussion replies on HN. Paper and source history. A submission is not an endorsement.