
Extending the Algebraic Manipulability of Differentials - panic
https://arxiv.org/abs/1801.09553
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quag
If you’re interested in automatic differentiation or manipulating
differentials, checkout the video on [http://conal.net/papers/essence-of-
ad/](http://conal.net/papers/essence-of-ad/)

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chobytes
With Robinson’s hyperreal numbers(1), I see no reason not to just freely use
infinitesimals again.

(1)[https://en.m.wikipedia.org/wiki/Hyperreal_number](https://en.m.wikipedia.org/wiki/Hyperreal_number)

~~~
earthicus
Differentials can be done rigorously simply using variables, as Cauchy showed
us 200 years ago. This is done in Stewart (standard undergrad textbook), in
addition to the limit/derivative approach and he freely uses them in proofs
and derivations throughout the book when they are more convenient.

As the article discusses, the difficulty in treating differentials
algebraically is how higher order derivatives behave. This problem exist in
Robinson's nonstandard analysis as well, and the authors of the paper point
this out at the end of section 2, along with examples in the literature. The
substance of the article is improving the notation of differentials so that
the actual algebraic properties of e.g. the chain rule appear sensible.

