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Title: Calculus: Concepts and Connections
ISBN: 007330929X
Author:
Robert Smith
Roland Minton
Publicate Date: 2007-05-23
Publish: 2007-05-23
List Price: $61.99
Average Customer Rating: 3.5
Format: Hardcover
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Amazon Lowest New Price: $61.99
Amazon Lowest Used Price: $35.91
Amazon Merchant Price: $185.00
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| Customer Review: |
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1: Good supplement
Another reviewer has pointed out some of the shortcomings of this text, and those are some pretty critical problems. I would not recommend this text alone, but it is a pretty good supplement. Specifically, I found the discussion of curvature to be brilliant.
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2: Nice book
Gave me a good understanding of Calculus concepts, I needed it to go through a pre-req for my Masters in Computer Science. Would give it a 4 star.
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3: not too good
-The definition of e is given as lim(1 + 1/n)^n, with no motivation, and before
limits are discussed. (From a book purporting to emphasize concepts!)
-No proof of the general power rule appears (it's an easy application of
logarithmic differentiation).
-No formula is given for the derivative of e^f(x).
-A "proof" of the mean value theorem appears in the appendix. It invokes
Rolle's theorem, but Rolle's theorem is not proven. (Reason: Rolle's uses the
extreme value theorem which is not mentioned in the book. It also uses
Fermat's theorem, which is not covered until 40 pages after Rolle's in this book.)
-Newton's method is introduced before students have experience solving
equations of the form f(x)=0 (e.g. finding critical numbers). So there is no
motivation. Also it is done before graphing, so students have no basis
for making their initial estimate.
-Part 1 of the fundamental theorem of calculus follows in 2 lines from part 2.
This text makes no mention of this; it gives separate proofs of each part
using the MVT.
In general, this text seems pretty disengaged from the underlying mathematics.
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