![]() ![]() 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. Thompson, revised by Martin Gardner, Calculus Made Easy (St. Carl Linderholm, College Mathematics Journal, Vol.41, doi: 10.1038/086041c0 a review of the first edition available here and here. Calculus Made Easy public domain audiobook at LibriVox.Calculus Made Easy at Project Gutenberg (Re-typeset in LaTeX).Also available as the (London: MacMillan and Co., Limited, 2nd Ed., 1914) printing, which isn't published under Thompson's name, but instead has the byline of "by F.R.S." (i.e., Fellow of the Royal Society) also available as a different scanning here. Thompson, Calculus Made Easy: Being a Very-Simplest Introduction to Those Beautiful Methods of Reckoning which Are Generally Called by the Terrifying Names of the Differential Calculus and the Integral Calculus (New York: MacMillan Company, 2nd Ed., 1914). It can be freely accessed on Project Gutenberg. The original text is now in the public domain under US copyright law (although Macmillan's copyright under UK law is reproduced in the 2008 edition from St. Gardner changes "fifth form boys" to the more American sounding (and gender neutral) "high school students," updates many now obsolescent mathematical notations or terms, and uses American decimal dollars and cents in currency examples.Ĭalculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern nonstandard analysis and smooth infinitesimal analysis. Martin's Press which provides an introduction three preliminary chapters explaining functions, limits, and derivatives an appendix of recreational calculus problems and notes for modern readers. The original text continues to be available as of 2008 from Macmillan and Co., but a 1998 update by Martin Gardner is available from St. Thompson, considered a classic and elegant introduction to the subject. ![]() If a curve is one that turns more upwards as it goes along to the right, the values of d y d x will become greater and greater with the increasing steepness.Ĭalculus Made Easy is a book on infinitesimal calculus originally published in 1910 by Silvanus P. ![]()
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