Hassan Sedaghat

Real Analysis and Infinity (eBook, PDF)

• Format: PDF

Produktbeschreibung

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. After introducing sequences of numbers, it develops the set of real numbers in terms of Cauchy sequences of rational numbers, and uses this development to derive the important properties of real numbers like completeness. The book then develops the concepts of continuity, derivative, and integral, and presents the theory of infinite sequences and series of functions. Topics discussed are wide-ranging and include the convergence of sequences, definition of limits and continuity via converging sequences, and the development of derivative. The proofs of the vast majority of theorems are presented and pedagogical considerations are given priority to help cement the reader's knowledge. Preliminary discussion of each major topic is supplemented with examples and diagrams, and historical asides. Examples follow most major results to improve comprehension, and exercises at the end of each chapter help with the refinement of proof and calculation skills.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Oxford University Press
• Seitenzahl: 464
• Erscheinungstermin: 7. März 2022
• Englisch
• ISBN-13: 9780192649539
• Artikelnr.: 63600130

Autorenporträt

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.

Inhaltsangabe

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