Classical analysis of real-valued functions /

Divided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to differential geometry, Fourier series, differential...

Ausführliche Beschreibung

Gespeichert in:
1. Verfasser:
Serov, Valery
Format:
Elektronisch E-Book
Sprache:
Englisch
Veröffentlicht:
Philadelphia, Pennsylvania : Alexandria, Virginia : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) ; American Statistical Association, [2023]
Zusammenfassung:
Divided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to differential geometry, Fourier series, differential equations, and other subjects. The first part of Classical Analysis of Real-Valued Functions covers the theorems of existence of supremum and infimum of bounded sets on the real line and the Lagrange formula for differentiable functions. Applications of these results are crucial for classical mathematical analysis, and many are threaded through the text. In the second part of the book, the implicit function theorem plays a central role, while the Gauss-Ostrogradskii formula, surface integration, Heine-Borel lemma, the Ascoli-Arzelà theorem, and the one-dimensional indefinite Lebesgue integral are also covered.
Umfang:
1 PDF (x, 412 pages).
Also available in print version.
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Format Details:
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Bibliografie:
Includes bibliographical references (page 407) and index.
ISBN:
9781611977677
DOI:
10.1137/1.9781611977677
Zugangseinschränkungen:
Restricted to subscribers or individual electronic text purchasers.
Schlagworte:
Harmonic analysis.
Differential equations.
MATHEMATICS / Functional Analysis.
MATHEMATICS / Numerical Analysis.
MATHEMATICS / Set Theory.
MATHEMATICS / Applied.
MATHEMATICS / History & Philosophy.
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