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Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts.
Table des matières
- Preface
- 1: Manifestations of Infinity: An Overview
- 2: Sets, Functions, Logic and Countability
- 3: Sequences and Limits
- 4: The Real Numbers
- 5: Infinite Series of Constants
- 6: Differentiation and Continuity
- 7: Integration
- 8: Infinite Sequences and Series of Functions
- Appendix: Cantor's Construction: Additional Detail
- Appendix: Discontinuity in a Space of Functions
- References and Further Reading
A propos de l'auteur
Hassan Sedaghat is Professor Emeritus of Mathematics at Virginia Commonwealth University, USA. He has over 35 years of teaching experience in college mathematics, from freshman to the postgraduate level. He is the author of three books and over 60 research papers in the areas of analysis and nonlinear difference equations. He has collaborated with many researchers throughout the world on work in many joint publications and has given numerous invited talks in local and international venues.
Résumé
Real Analysis and Infinity presents the essential topics for a first course in real analysis with an emphasis on the role of infinity in all of the fundamental concepts.
Texte suppl.
This attractively produced book covers all of the topics one would expect to find in an introductory text on real analysis. Thus a short scene-setting chapter is followed by a background chapter on sets, functions, logic and countability and then six long chapters on sequences and limits, the real numbers (constructed in detail using Q-Cauchy sequences), infinite series, differentiation and continuity (in that order), Riemann integration (using the Darboux formulation) and infinite series of functions.
