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Introductory Analysis
The Theory of Calculus
2nd Edition - January 10, 2000
Author: John A. Fridy
Language: English
Hardback ISBN:9780122676550
9 7 8 - 0 - 1 2 - 2 6 7 6 5 5 - 0
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…Read more
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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
Researchers, professionals, the general public, and librarians who want to expand or enhance their knowledge of calculus limit theories
Introduction: Mathematical Statements and Proofs Ordering of the Real Numbers Sequence Limits Completeness of the Real Numbers Continuous Functions Consequences of Continuity The Derivative The Riemann Integral Improper Integrals Infinite Series The Riemann-Stieltjes Integral Function Sequences Power Series Metric Spaces and Euclidean Spaces Continuous Transformations Differential Calculus in Euclidean Spaces Area and Integration in E²
Appendix A. Mathematical Induction B. Countable and Uncountable Sets C. Infinite Products