Introduction to Real Analysis - Brossura

Schramm, Michael J.

Brossura

ISBN 10: 0486469131 ISBN 13: 9780486469133

Casa editrice: Dover Pubns, 2009

Riassunto

This text forms a bridge between courses in calculus and real analysis. It focuses on the construction of mathematical proofs as well as their final content. Suitable for upper-level undergraduates and graduate students of real analysis, it also provides a vital reference book for advanced courses in mathematics.The four-part treatment begins with an introduction to basic logical structures and techniques of proof, including discussions of the cardinality concept and the algebraic and order structures of the real and rational number systems. Part Two presents in-depth examinations of the completeness of the real number system and its topological structure. Part Three reviews and extends the previous explorations of the real number system, and the final part features a selection of topics in real function theory. Numerous and varied exercises range from articulating the steps omitted from examples and observing mechanical results at work to the completion of partial proofs within the text.

Su questo libro

L'autore:

Michael J. Schramm has a Ph.D. from Syracuse University.

Contenuti:

Preface Part One: Preliminaries Chapter 1. Building Proofs Chapter 2. Finite, Infinite, and Even Bigger Chapter 3. Algebra of the Real Numbers Chapter 4. Ordering, Intervals, and Neighborhoods Part Two: The Structure of the Real Number System Chapter 5. Upper Bounds and Suprema Chapter 6. Nested Intervals Chapter 7. Cluster Points Chapter 8. Topology of the Real Numbers Chapter 9. Sequences Chapter 10. Sequences and the Big Theorem Chapter 11. Compact Sets Chapter 12. Connected Sets Part Three: Topics from Calculus Chapter 13. Series Chapter 14. Uniform Continuity Chapter 15. Sequences and Series of Functions Chapter 16. Differentiation Chapter 17. Integration Chapter 18. Interchanging Limit Processes Part Four: Selected Shorts Chapter 19. Increasing Functions Chapter 20. Continuous Functions and Differentiability Chapter 21. Continuous Functions and Integrability Chapter 22. We Build the Real Numbers References and further reading Index

Su questa edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2009
• ISBN 10: 0486469131
• ISBN 13: 9780486469133
• Rilegatura: Copertina flessibile
• Numero di pagine: 369