I am very interested in learning about the conditions under which a function can be integrated in elementary terms, a topic that I understand falls within the purview of differential algebra. Having looked at a few of the "classical" textbooks, like Kolchin and Kaplansky, and after some skimming I realised that most of the material would probably go over my head. Is there a more accessible resource (book or article or anything) that I could use as a primer before tackling these books? I've had the standard calculus sequence, know linear algebra pretty well, don't know much ring/field theory though I'm afraid. Would this suffice?
2026-03-25 04:36:34.1774413394
Accessible first book/resource on differential algebra
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You can try the paper The Problem of Integration in finite terms by R. H. Risch, I think the first chapter should cover what you need. The author writes that he learned this from the book Integration in finite terms - Liouville's theory of elementary functions from Ritt, so this might be worth a look as well.