Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) ; Alexandria, Virginia : American Statistical Association, [2023]
Restricted to subscribers or individual electronic text purchasers.
Summary note
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-ArzelaÌ theorem, and the one-dimensional indefinite Lebesgue integral are also covered.
Bibliographic references
Includes bibliographical references (page 407) and index.
System details
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Source of description
Description based on title page of print version.
Contents
part I. Analysis of numbers and functions of one variable. Introduction
Real numbers
Theory of limits of real numbers
Series and infinite products of real numbers
Continuity of one-variable functions
Differentiation
Taylor's expansion and its applications
Indefinite Riemann integral
Riemann-Stieltjes integral
Improper integrals
Approximate methods
part II. Analysis of multivariable functions and Lebesgue integration. Geometric applications of integrals. Elementary measure theory
Continuity and differentiability of functions of several variables
Implicit functions
Multidimensional Riemann integrals
Lebesgue integration
Continuity in Banach spaces. Topological concepts.
Other format(s)
Also available in print version.
ISBN
1-61197-767-3
Publisher no.
OT193
LCCN
2023018601
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