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Real Analysis for the Undergraduate [electronic resource] :With an Invitation to Functional Analysis / by Matthew A. Pons.

by Pons, Matthew A [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: New York, NY : Springer New York : 2014.Description: XVIII, 409 p. 43 illus. online resource.ISBN: 9781461496380.Subject(s): Mathematics | Global analysis (Mathematics) | Functional analysis | Mathematics | Analysis | Real Functions | Functional AnalysisDDC classification: 515 Online resources: Click here to access online
Contents:
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 .
In: Springer eBooksSummary: 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.
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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.

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