Introductory Analysis: The Theory of Calculus Book

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 abstractNew 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 symbolsRead More