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Elements Of Real Analysis : International Series in Mathematics - Charles G. Denlinger

Elements Of Real Analysis

International Series in Mathematics


Published: 22nd May 2010
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Elementary Real Analysis is a core course in nearly all mathematics departments throughout the world. It enables students to develop a deep understanding of the key concepts of calculus from a mature perspective. Elements of Real Analysis is a student-friendly guide to learning all the important ideas of elementary real analysis, based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors. It avoids the compact style of professional mathematics writing, in favor of a style that feels more comfortable to students encountering the subject for the first time. It presents topics in ways that are most easily understood, yet does not sacrifice rigor or coverage.

In using this book, students discover that real analysis is completely deducible from the axioms of the real number system. They learn the powerful techniques of limits of sequences as the primary entry to the concepts of analysis, and see the ubiquitous role sequences play in virtually all later topics. They become comfortable with topological ideas, and see how these concepts help unify the subject. Students encounter many interesting examples, including "pathological" ones, that motivate the subject and help fix the concepts. They develop a unified understanding of limits, continuity, differentiability, Riemann integrability, and infinite series of numbers and functions.

Preface To The Student To The Instructor Chapter 1: The Real Number System Chapter 2: Sequences Chapter 3: Topology of the Real Number System Chapter 4: Limits of Functions Chapter 5: Continuous Functions Chapter 6: Differentiable Functions Chapter 7: The Riemann Integral Chapter 8: Infinite Series of Real Numbers Chapter 9: Sequences and Series of Functions Appendix A Logic and Proofs Appendix B Sets and Functions Appendix C Answers and Hints for Selected Exercises Bibliography Glossary of Symbols Index

ISBN: 9780763779474
ISBN-10: 0763779474
Series: International Series in Mathematics
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 739
Published: 22nd May 2010
Publisher: Jones and Bartlett Publishers, Inc
Country of Publication: US
Dimensions (cm): 23.8 x 19.4  x 4.3
Weight (kg): 1.13
Edition Number: 1
Edition Type: New edition