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Calculus refresher

AuthorPaul Garrett Entered2004-01-08 10:49:58 by Ryanov
Editedit data record FreedomCopylefted: anyone can read, modify, and sell (disclaimer)
SubjectQ.A - Mathematics. Computer science (analysis)
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http://www.math.umn.edu/~garrett/calculus/
This link was reported to be OK by user Ben Crowell on 2004-01-11 11:29:52
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more than lecture notes, less than a stand-alone text
by Ben Crowell (crowell09 at stopspam.lightandmatter.com (change 09 to current year)) on 2014-06-03 10:26:33, review #547
http://www.lightandmatter.com
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typical
writing
typical
This is a lively and very readable treatment of basic calculus. At 70 pages, it's a welcome antidote to the usual bloated textbooks, and the topics that are included match up pretty well with my own opinions of what it's really vital for a student to know after taking a calculus course. The tone is conversational without being condescending or cutesy, and the author almost always explains why he's introducing something, rather than just throwing it at the reader. (An unfortunate exception is the opening section on inequalities.) There is no attempt at rigor whatsoever, which I consider to be a feature, not a bug. Applications are discussed, although not enough for my taste (and I have to suppress my gag reflex every time I see a calculus book that insists on presenting the acceleration of gravity in non-metric units).

Although the book comes with some of the paraphernalia of a complete college textbook, such as homework problems, it's probably not the kind of book that another professor could just adopt as a stand-alone text, nor would I recommend it for someone learning calculus on her own for the first time. The title is given as "Notes on first-year calculus," which suggests that the author had in mind more of a memory aid, or a way to keep students from having to scribble madly in their notebooks for an hour and a half at a stretch. It lacks an index and illustrations, and there are some misfeatures in terms of organization: the chapters aren't numbered, and the homework problems are scattered around where they're hard to find. In some cases it sounds as though the first time a word or concept is used, he's assuming the reader has already heard it defined. I would, however, recommend this book to someone who needs to refresh her memory of calculus, and doesn't want to spend hours wading through epsilons and deltas to get to the highlights. It might also be a good option for the student who is completely broke, and needs a reference to use in place of an officially required text that carries an exploitative price tag.

The book is provided in PDF format, and LaTeX source code is also distributed. The license is CC-BY.

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