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Introductory Analysis, Second Edition: The Theory of Calculus

 
 
 
 
Introductory Analysis, Second Edition: The Theory of Calculus
Author: John A. Fridy
ISBN 13: 9780122676550
ISBN 10: 122676556
Edition: 2
Publisher: Academic Press
Publication Date: 2000-01-24
Format: Hardcover
Pages: 335
List Price: $137.00
 
 

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

Booknews

Contains a theoretical development of the calculus concepts that are presented intuitively in the typical freshman/sophomore calculus course, intended as a text for a theory course usually taken in the junior or senior year. Material is held at a reasonable level for undergraduates by presenting most of the theory in the familiar real number system as opposed to a more general or abstract setting. Expository style of the book is intended to illustrate formal mathematical writing as opposed to the informality frequently found in freshman texts. The author is affiliated with Kent State University. Annotation c. Book News, Inc., Portland, OR (booknews.com)