Monday, July 20, 2009


The Calculus Integral [Beta0.2],
B S Thomson, (2009)

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Well "calculus book" doesn't quite describe it. It is an account of integration theory on the real line that starts in the initial chapters with the "calculus integral" (i.e., the original integral of Newton) and carries the development as far as the integrals of Lebesgue and Henstock-Kurzweil.

If you are, however, teaching a calculus course and have ever considered dropping the Riemann integral and its ugly step-sister the improper Riemann integral from the syllabus, then you might want to use the first three chapters as a basis for the teaching of the basic integral of the calculus.

A trade paperback version will be available shortly.


ChristianTrader said...

Is this book a "replacement" for your regular elementary real analysis book (or at least your DRIP version) or are they complementary?

Brian S Thomson said...

Hi Christian,

The regular [TBB] Elementary Real Analysis still stands as an introductory course textbook using the conventional Riemann and improper Riemann integrals. [Drip] just replaces all the integration theory with the Henstock-Kurzweil integration, but otherwise is the same text.

The new one [The Calculus Integral] is closer to [Drip] in most ways. It starts with the original eighteenth century Newton integral and develops that as a starting point for integration theory on the real line. After a few chapters it transitions to an
account of the Lebesgue integral and the Henstock-Kurzweil integral.

The main feature is that the first three chapters could be used to teach all of the usual calculus integration theory without committing to the Riemann integral as is usually the case.

Good luck,

Anonymous said...


Will you guys publish/provide solutions for exercises in "Elementary Real Analysis"?


Brian S Thomson said...

>>Will you guys publish/provide >>solutions for exercises in
>>"Elementary Real Analysis"?

I don't think so. If sales pick up and we can afford that Chateau in France we will use that leisure time to prepare solutions. At the moment sales cover the odd bottle of "Chateau" Gallo.

But maybe a discussion group would do the same thing. Have you tried posting questions from the text on any?