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Real Analysis: Foundations

Real Analysis: Foundations

Autorzy
Wydawnictwo Springer Nature Customer Service Center GmbH
Data wydania 01/02/2021
Wydanie Pierwsze
Liczba stron 178
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
Język angielski
ISBN 9783030647001
Kategorie Podstawy matematyki, Analizy realne i zmienne rzeczywiste, Rachunek całkowy
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Opis książki

This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.

Real Analysis: Foundations

Spis treści

1 Rational Numbers.- 2 Real Numbers.- 3 Continuous Functions.- 4 Differentiation.- 5 Integration.- 6 Infinite Series.- A Natural Numbers and Integers.- B Dedekind's Construction of Real Numbers. C A Panorama of Ordered Fields.

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