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Infinitesimal Calculus (Dover Books on Mathematics)

James M. Henle, Eugene M. Kleinberg · 4 HN comments
HN Books has aggregated all Hacker News stories and comments that mention "Infinitesimal Calculus (Dover Books on Mathematics)" by James M. Henle, Eugene M. Kleinberg.
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Amazon Summary
Rigorous undergraduate treatment introduces calculus at the basic level, using infinitesimals and concentrating on theory rather than applications. Requires only a solid foundation in high school mathematics. Contents: 1. Introduction. 2. Language and Structure. 3. The Hyperreal Numbers. 4. The Hyperreal Line. 5. Continuous Functions. 6. Integral Calculus. 7. Differential Calculus. 8. The Fundamental Theorem. 9. Infinite Sequences and Series. 10. Infinite Polynomials. 11. The Topology of the Real Line. 12. Standard Calculus and Sequences of Functions. Appendixes. Subject Index. Name Index. Numerous figures. 1979 edition.
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This is one book on infinitesimal calculus: https://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Ma... .

However, and this is very amusing to me, it turns out that the process of automatic differentiation (see https://en.wikipedia.org/wiki/Automatic_differentiation, the section on dual numbers) works in exactly the same way. Just replace all of the primed symbols (u', v', etc.) with du, dv, etc. and dual numbers are isomorphic to infinitesimals (if I'm using that term correctly.)

Looks similar to this book, which I bought after a recommendation here: https://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Ma...
While I haven't examined it closely, there's a well thought of, concise, no-fluff book on it: http://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Mat...
One more book I found to be useful, at least for its introduction to the hyperreal number system: http://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Mat... It's short and focused.
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