Thompson and anyone who has already learned calculus can make sense of it in hindsight, but how can it be viewed as anything but nonsense by a first-time reader? Some of the other books listed in comments are far better imo. What's a beginning student supposed to make of this? But wait, we can make that flea $dx$ as small as we wish, and a flea as small as we wish certainly wouldn't bother an ox. As a real world example, we're told to think of $dx$ as a flea on an ox (which would bother the ox) and $(dx)^2$ as a flea on the flea (which wouldn't bother the ox). It leads to wonderful chains of reasoning such as $y+dy=x^2+2x\cdot dx+(dx)^2$ but let's drop the small term (no, not that one.the really small one dummy) and actually $y+dy=x^2+2x\cdot dx$. I'm not being unfair either, this is the actual essence of his argument. I looked at the second edition (not the Gardner update), but unless Gardner practically rewrote the book I don't think this matters much.Īt the very beginning, derivatives are explained by simply stating that $dx$ is small and so $(dx)^2$ and higher powers are, like, really really small and they don't matter so we ignore them. You may also be interested in my own textbook Fundamentals of Calculus, which introduces both infinitesimals and limits while focusing mainly on techniques and applications rather than foundational issues.Īfter giving the book another look I have to expand on my comment above and make it stronger: no, this isn't a good book for a first-time learner, and in fact I think it's a terrible choice. Compared to Thompson, it's boring and pedantic and slow and lacking in personality, but it's worth having on hand while working through Thompson. There is a text by Keisler that is free online and introduces freshman calculus using infinitesimals, but with a bit more of the modern machinery. When teaching yourself something intellectually challenging, I would always suggest that you find multiple sources of information rather than just focusing on one book. Historically, there were some concerns that infinitesimals were inherently inconsistent, but it turns out that that's not the case. Both infinitesimals and limits are perfectly fine ways of introducing calculus. It uses infinitesimals rather than limits. IIRC Gardner moderates some of the dated and sexist language.īe aware of how this book's approach relates to the history and to currently fashionable ways of presenting calculus. It cuts out a ton of the ridiculous cruft that has clogged up the current crop of commercial freshman calculus texts.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |