Basic Real Analysis

by Anthony W. Knapp

Overview

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.

Product Details

ISBN-13:	9780817632502
Publisher:	Birkhäuser Boston
Publication date:	07/29/2005
Series:	Cornerstones
Edition description:	2005
Pages:	656
Product dimensions:	6.10(w) x 9.25(h) x 0.06(d)

Table of Contents

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.

Editorial Reviews

From the reviews:

“The volume contains more than 300 problems and a separate section gives hints or complete solutions to them. The book seems to be completely unified, carefully reasoned, rich in concepts, methods and results, and indubitably useful as for students in Real Analysis so also for teachers in this field.”(Zentralblatt MATH)

"This book tries to develop concepts and tools in real analysis that are vital to every mathematician. … The book contains more than 300 problems with hints and complete solutions for many of them." (A. Kriegl, Monatshefte für Mathematik, Vol. 151 (3), 2007)

From the Publisher