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The Real Numbers and Real Analysis

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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.

Author(s): Ethan D. Bloch
Publisher: Springer Science & Business Media
Year: 2011

Language: English
Pages: 577

The Real Numbers and Real Analysis
Contents
Preface
To the Student
To the Instructor
1 Construction of the Real Numbers
2 Properties of the Real Numbers
3 Limits and Continuity
4 Differentiation
5 Integration
6 Limits to Infinity
7 Transcendental Functions
8 Sequences
9 Series
10 Sequences and Series of Functions
Bibliography
Index