The Real Numbers and Real Analysis

• Main Author: Bloch, Ethan D. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2011.
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Functions of real variables.; Sequences (Mathematics).; Real Functions.; Analysis.; Sequences, Series, Summability.

This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs.  The choice of material and the flexible organization, including three different entryways into the study of the real numbers,...

Table of 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. Transcental Functions.-8. Sequences
• 9. Series
• 10. Sequences and Series of Functions
• Bibliography
• Index.