A COURSE IN REAL ANALYSIS

Le Monde En Tique

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Ouvrage 0-12-742830-5 : A COURSE IN REAL ANALYSIS
A Course in Real Analysis provides a firm foundation in real analysis concepts and principles while presenting a broad range of topics in a clear and concise manner. Taking a student-oriented approach, Professors McDonald and Weiss have written a text that balances theory and applications and contains a wealth of examples and exercises.
Throughout the text, the authors adhere to the idea that most students learn more efficiently by passing from the concrete to the abstract. The authors have also created real application chapters on probability theory, harmonic analysis, and dynamical systems theory. The text offers considerable flexibility in the choice of material to cover.
From Booknews:
A textbook for a one-year course at the graduate or advanced undergraduate level, incorporating pedagogical techniques not often found in such treatments. Encompasses set theory, real numbers, and calculus; measure, integration, and differentiation; topological, metric, and normed spaces; and harmonic analysis and dynamical systems. Suggests various ways of presenting the material. Includes a biographical sketch of a famous mathematician at the beginning of each chapter. No bibliography. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Table of Contents Preface
Pt. 1
Set Theory, Real Numbers, and Calculus
1
Set Theory
Biography: Georg Cantor 2
The Real Number System and Calculus Biography: Georg Friedrich Bernhard Riemann
Pt. 2
Measure, Integration, and Differentiation
3
Lebesgue Theory on the Real Line Biography: Emile Felix-Edouard-Justin Borel
4
Measure Theory
Biography: Henri Leon Lebesgue 5
Elements of Probability Biography: Andrei Nikolaevich Kolmogorov
6
Differentiation
Biography: Johann Radon Pt. 3
Topological, Metric, and Normed Spaces
7
Elements of Topological, Metric, and Normed Spaces
Biography: Pavel Samuilovich Urysohn 8
Complete Spaces, Compact Spaces, and Approximation
Biography: Marshall Harvey Stone 9
Hilbert Spaces and the Classical Banach Spaces
Biography: David Hilbert 10
Basic Theory of Normed and Locally Convex Spaces
Biography: Stefan Banach Pt. 4
Harmonic Analysis and Dynamical Systems
11
Elements of Harmonic Analysis Biography: Ingrid Daubechies 12
Measurable Dynamical Systems Biography: Claude Elwood Shannon Index

Auteur : MC DONALD
Editeur : ACADEMIC PRESS
Nombre de pages : 720
Date de publication : 02 1999

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