"Introductory Analysis, Second Edition," is intended for the
standard course on calculus limit theories that is taken after a
problem solving first course in calculus (most often by
junior/senior mathematics majors). Topics studied include
sequences, function limits, derivatives, integrals, series, metric
spaces, and calculus in n-dimensional Euclidean space
* Bases most of the various limit concepts on sequential limits,
which is done first
* Defines function limits by first developing the notion of
continuity (with a sequential limit characterization)
* Contains a thorough development of the Riemann integral, improper
integrals (including sections on the gamma function and the Laplace
transform), and the Stieltjes integral
* Presents general metric space topology in juxtaposition with
Euclidean spaces to ease the transition from the concrete setting
to the abstract
New to This Edition
* Contains new Exercises throughout
* Provides a simple definition of subsequence
* Contains more information on function limits and L'Hospital's
Rule
* Provides clearer proofs about rational numbers and the integrals
of Riemann and Stieltjes
* presents an appendix lists all mathematicians named in the
text
* Gives a glossary of symbols
General
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