From Classical to Modern Analysis

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Sprache: Englisch

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Beschreibung

This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual, From Classical to Modern Analysis is a comprehensive, yet straightforward, resource for studying real analysis.

To build the foundational elements of real analysis, the first seven chapters cover number systems, convergence of sequences and series, as well as more advanced topics like superior and inferior limits, convergence of functions, and metric spaces. Chapters 8 through 12 explore topology in and continuityon metric spaces and introduce the Lebesgue integrals. The last chapters are largely independent and discuss various applications of the Lebesgue integral.

Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.

Über den Autor

Rinaldo Schinazi is a Professor of Mathematics at the University of Colorado, USA.

Zusammenfassung

Guides undergraduate students from calculus to measure theory and the Lebesgue integral

Provides a self-contained presentation of metric spaces and their topology tailored for first-time students of real analysis

Includes cumulative exercises that prepare students for real analysis's many applications

Inhaltsverzeichnis

Preface.- Real Numbers.- Sequences of Real Numbers.- Limits Superior and Inferior of a Sequence.- Numerical Series.- Convergence of Functions.- Power Series.- Metric Spaces.- Topology in a Metric Space.- Continuity on Metric Spaces.- Measurable Sets and Measurable Functions.- Measures.- The Lebesgue Integral.- Integrals with Respect to Counting Measures.- Riemann and Lebesgue Integrals.- Modes of Convergance.- References.

Details

Erscheinungsjahr:	2018
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xii 270 S. 1 s/w Illustr. 270 p. 1 illus.
ISBN-13:	9783319945828
ISBN-10:	3319945823
Sprache:	Englisch
Herstellernummer:	978-3-319-94582-8
Einband:	Gebunden
Autor:	Schinazi, Rinaldo B.
Auflage:	1st edition 2018
Hersteller:	Springer International Publishing Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	241 x 160 x 21 mm
Von/Mit:	Rinaldo B. Schinazi
Erscheinungsdatum:	04.10.2018
Gewicht:	0,594 kg

Artikel-ID: 113780785