The Real Numbers and Real Analysis

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Springer Science & Business Media, May 19, 2011 - Mathematics - 553 pages
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This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus.

The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.

  

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Contents

1 Construction of the Real Numbers
1
2 Properties of the Real Numbers
61
3 Limits and Continuity
129
4 Differentiation
181
5 Integration
231
6 Limits to Infinity
321
7 Transcendental Functions
356
8 Sequences
399
9 Series
443
10 Sequences and Series of Functions
488
Bibliography
539
Index
544
Copyright

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About the author (2011)

Dr. Ethan D. Bloch of Bard College is the author of two Springer publications "A First Course in Geometric Topology and Differential Geometry," and the first and second editions of, "Proofs and Fundamentals: A First Course in Abstract Mathematics." More information about Dr. Ethan D. Bloch can be found on his person web page: http://math.bard.edu/bloch

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