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Calculus Bible, The

AuthorG. S. Gill Entered2002-05-05 06:18:51 by kalkibagawan
Editedit data record FreedomCopyrighted, doesn't cost money to read, but otherwise not free (disclaimer)
SubjectQ.A - Mathematics. Computer science (analysis)
This link was reported to be broken by user Vignesh ramesh on 2012-04-29 20:43:06
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dry, and short on applications and motivation
by Ben Crowell (crowell09 at (change 09 to current year)) on 2004-03-02 21:13:57, review #386
I'm reviewing this book in February of 2004. It's clearly not a finished product, and I'm not sure whether or not the author is still actively working on it. The book is available from the Brigham Young University math department's server, but the author isn't on the department's list of faculty, which makes me think he may have moved on to another job and abandoned the book. It's provided as a PDF file. There is no copyright page and no licensing agreement, so it's hard to know the book's real legal status.

The path through the topics is pretty standard for an introductory calculus course: a review of functions and trigonometry, followed by limits, differentiation, and integration. There is a good selection of problems, although to my taste as a physicist far too few are applied to anything useful. There is a table of contents, but no index. There are no illustrations; sprinkled throughout the text are little placeholders for graphs that just say "graph." The lack of an index or illustrations is the reason I've rated the book as substandard in the writing category.

Although the problems I've referred to so far are ones that could be fixed if the author continued to work on the book, I feel that there are some more fundamental problems with this text that will not go away unless it is extensively rewritten. The style is extremely dry, and moreover the author has a habit of introducing concepts without any explanation or preparation. A symptom of this is that the student is expected to grind through the first hundred pages without any clear statement about what calculus is, what it's good for, or even whether the initial chapters are calculus (they're not). Equal prominence is given to topics that I would consider vital (the fundamental theorem of calculus) and others that I would label as trivial (tabulations of facts) or esoteric (the Dedekind cut property).

The Leibniz notation, dy/dx, is given with only this explanation "To emphasize the fact that the derivatives are taken with respect to the independent variable x, we use the following notration, as is customary..." Huh? So are these dx and dy things numbers? Is dy/dx the quotient of them?

Even if the missing graphs were included, the approach would still be relentlessly symbolic, rather than visual. For instance, integration by parts is introduced without ever giving its geometric interpretation.

In summary, I think this is a poor book, and even if you're looking for a free calculus textbook, there are better options.

Information wants to be free, so make some free information.

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