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" Real analysis for the undergraduate : "
Matthew A. Pons with illustrations by Robert F. Allen.
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BL
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| Record Number
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644105
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| Doc. No
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dltt
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| Main Entry
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Pons, Matthew A.
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| Title & Author
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Real analysis for the undergraduate : : with an invitation to functional analysis /\ Matthew A. Pons with illustrations by Robert F. Allen.
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| Page. NO
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xviii, 409 pages :: illustrations ;; 24 cm
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| ISBN
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9781461496373
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: 1461496373
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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1. The real numbers -- 2. Sequences in R -- 3. Numerical series -- 4. Continuity -- 5. The derivative -- 6. Sequences and series of functions -- 7. The Riemann integral -- 8. Lebesgue measure on R -- 9. Lebesgue integration.
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| Abstract
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This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author's engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: examples to reinforce theory; thorough explanations preceding definitions, theorems and formal proofs; illustrations to support intuition; over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum.
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| Subject
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Global analysis (Mathematics)
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| Subject
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Functional analysis.
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Mathematics.
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| Dewey Classification
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515
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| LC Classification
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QA299.6.P667 2014
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| Added Entry
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Allen, Robert F.
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