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＜E-Book＞
Real Analysis for the Undergraduate : With an Invitation to Functional Analysis / by Matthew A. Pons

Edition	1st ed. 2014.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2014
Language	English
Size	XVIII, 409 p. 43 illus : online resource
Authors	*Pons, Matthew A author SpringerLink (Online service)
Subjects	LCSH:Mathematical analysis LCSH:Functions of real variables LCSH:Functional analysis FREE:Analysis FREE:Real Functions FREE:Functional Analysis
Notes	The Real Numbers -- Sequences in R -- Numerical Series -- Continuity -- The Derivative -- Sequence and Series of Functions -- The Riemann Integral -- Lebesgue Measure on R -- Lebesgue Integration This undergraduate textbook introduces students to the basics of real analysis, provides an introduction to more advanced topics including measure theory and Lebesgue integration, and offers an invitation to functional analysis. While these advanced topics are not typically encountered until graduate study, the text is designed for the beginner. The author’s engaging style makes advanced topics approachable without sacrificing rigor. The text also consistently encourages the reader to pick up a pencil and take an active part in the learning process. Key features include: - examples to reinforce theory; - thorough explanations preceding definitions, theorems and formal proofs; - illustrations to support intuition; - over 450 exercises designed to develop connections between the concrete and abstract. This text takes students on a journey through the basics of real analysis and provides those who wish to delve deeper the opportunity to experience mathematical ideas that are beyond the standard undergraduate curriculum HTTP:URL=https://doi.org/10.1007/978-1-4614-9638-0

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