Basic Real Analysis

2005. Auflage 2005
ISBN: 978-0-8176-3250-2
Verlag: Birkhauser Boston

Buch, Englisch, 656 Seiten, Format (B × H): 159 mm x 244 mm, Gewicht: 1136 g

Reihe: Cornerstones

Basic Real Analysis systematically develops those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. Along with a companion volume Advanced Real Analysis (available separately or together as a Set), these works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.

Basic Real Analysis requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advanced undergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate studentspreparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Basic Real Analysis make it a welcome addition to the personal library of every mathematician.

Zielgruppe

Graduate

Autoren/Hrsg.

Knapp, Anthony W

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe

Inhaltsverzeichnis

Theory of Calculus in One Real Variable.- Metric Spaces.- Theory of Calculus in Several Real Variables.- Theory of Ordinary Differential Equations and Systems.- Lebesgue Measure and Abstract Measure Theory.- Measure Theory for Euclidean Space.- Differentiation of Lebesgue Integrals on the Line.- Fourier Transform in Euclidean Space.- Lp Spaces.- Topological Spaces.- Integration on Locally Compact Spaces.- Hilbert and Banach Spaces.