Preliminary version of a new real analysis textbook is now available for free download. Free Download for BETA version.
|
 | THE CALCULUS INTEGRAL,
B. S. Thomson,
ClassicalRealAnalysis.com (2010).
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This is preliminary (I mean
really preliminary) and users should take on the obligation of feeding back any suggestions and corrections to me at
thomson@sfu.ca.
We get many visitors to this site who are seeking calculus materials but find here, instead, rather more severe real analysis textbooks. This text,
The Calculus Integral, is at the level of an honours calculus text and discusses in the initial chapters the simple integration theory on the real line that arises from using the original Newton integral. This integral is, arguably, a better teaching integral than the Riemann integral and better prepares the student for the modern theories of integration.
If you are a student of the calculus and just seeking other textbooks that cover the material of the standard calculus course you might find this too unusual. But you can read it, nonetheless, with this viewpoint: your course uses the Riemann integral and the improper Riemann integral --this course uses just the simpler calculus integral. Any serious student of mathematics should be able to manage thinking about two closely related integration theories at the same time. You will have to do this eventually anyway.
Note for fans of the DRIP program: This text adopts the point of view of the DRIP program that the Riemann integral should be dumped from undergraduate instruction excepting for occasional historical remarks. Rather than presenting immediately the correct theory of integration on the real line, we use the calculus integral as a warm-up. The student learns all the essentials of the integral without wasting time on the definition of the Riemann integral.