Elementary analysis : the theory of calculus
Author(s)
Bibliographic Information
Elementary analysis : the theory of calculus
（Undergraduate texts in mathematics）
Springer Science+Business Media, c2010
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Note
Includes bibliographical references and indexes
Description and Table of Contents
Description
Designed for students having no previous experience with rigorous proofs, this text can be used immediately after standard calculus courses. It is highly recommended for anyone planning to study advanced analysis, as well as for future secondary school teachers. A limited number of concepts involving the real line and functions on the real line are studied, while many abstract ideas, such as metric spaces and ordered systems, are avoided completely. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics, and optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.
Table of Contents
Introduction.- Sequences.- Continuity.- Sequences and Series of Functions.- Differentiation.- Integration.- Appendix on Set Notation.- Selected Hints and Answers
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