Introductory Analysis: A Deeper View of Calculus - ISBN:0120725509

Introductory Analysis: A Deeper View of Calculus

Date: 06 May 2011, 01:10

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Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.
* Written in an engaging, conversational tone and readable style while softening the rigor and theory
* Takes a realistic approach to the necessary and accessible level of abstraction for the secondary education students
* A thorough concentration of basic topics of calculus
* Features a student-friendly introduction to delta-epsilon arguments
* Includes a limited use of abstract generalizations for easy use
* Covers natural logarithms and exponential functions
* Provides the computational techniques often encountered in basic calculus
Summary: an informal tone for a broader audience
Rating: 4
There are many ways to teach calculus. Typically, for maths majors, a rigorous epsilon-delta approach has been favoured. So we get the classic texts by Spivak, Apostol and Marsden, for example. But a problem is that this approach often turns off many students who need a firm understanding of calculus and classical analysis. They may not be maths majors. Instead, they could be majoring in engineering or the physical sciences. So Bagby offers them a more informal approach.
He does not deprecate rigour. But by presenting his narrative in a casual way, he gains the flexibility in recasting important concepts of proofs in a way understandable to more readers.
Even maths majors may want to consider having his text, as a backup to their more formal books. Because sometimes the arguments given in the latter's proofs can be very difficult to understand and generalise.
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