A Course in Real Analysis

A Course in Real Analysis

2nd Edition - January 10, 2012

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  • Authors: John McDonald, Neil Weiss
  • Hardcover ISBN: 9780123877741

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Description

The second edition of A Course in Real Analysis provides a solid foundation of real analysis concepts and principles, presenting a broad range of topics in a clear and concise manner. The book is excellent at balancing theory and applications with a wealth of examples and exercises. The authors take a progressive approach of skill building to help students learn to absorb the abstract. Real world applications, probability theory, harmonic analysis, and dynamical systems theory are included, offering considerable flexibility in the choice of material to cover in the classroom. The accessible exposition not only helps students master real analysis, but also makes the book useful as a reference.

Key Features

  • New chapter on Hausdorff Measure and Fractals
  • Key concepts and learning objectives give students a deeper understanding of the material to enhance learning
  • More than 200 examples (not including parts) are used to illustrate definitions and results
  • Over 1300 exercises (not including parts) are provided to promote understanding
  • Each chapter begins with a brief biography of a famous mathematician

Readership

One- or two- semester course in real analysis for upper-level undergraduate and graduate students in mathematics, applied mathematics, computer science, engineering, economics, and physics

Table of Contents

  • 1. Set Theory
    2. The Real Number System and Calculus
    3. Lebesgue Measure on the Real Line
    4. The Lebesgue Integral on the Real Line
    5. Elements of Measure Theory
    6. Extensions to Measures and Product Measure
    7. Elements of Probability
    8. Differentiation and Absolute Continuity
    9. Signed and Complex Measures
    10. Topologies, Metrics, and Norms
    11. Separability and Compactness
    12. Complete and Compact Spaces
    13. Hilbert Spaces and Banach Spaces
    14. Normed Spaces and Locally Convex Spaces
    15. Elements of Harmonic Analysis
    16. Measurable Dynamical Systems
    17. Hausdorff Measure and Fractals

Product details

  • No. of pages: 688
  • Language: English
  • Copyright: © Academic Press 2012
  • Published: January 10, 2012
  • Imprint: Academic Press
  • Hardcover ISBN: 9780123877741

About the Authors

John McDonald

Affiliations and Expertise

Arizona State University, Tempe, U.S.A.

Neil Weiss

Neil Weiss
Neil A. Weiss (deceased) received his Ph.D. from UCLA and subsequently accepted an assistant-professor position at Arizona State University (ASU), where he was ultimately promoted to the rank of full professor. Weiss has taught mathematics, probability, statistics, and operations research from the freshman level to the advanced graduate level.

In recognition of his excellence in teaching, he received the Dean’s Quality Teaching Award from the ASU College of Liberal Arts and Sciences. He has also been runner-up twice for the Charles Wexler Teaching Award in the ASU School of Mathematical and Statistical Sciences. Weiss’s comprehensive knowledge and experience ensures that his texts are mathematically accurate, as well as pedagogically sound.

Weiss has published research papers in both theoretical and applied mathematics, including probability, engineering, operations research, numerical analysis, and psychology. He has also published several teaching-related papers.

In addition to his numerous research publications, Weiss has authored or coauthored books in real analysis, probability, statistics, and finite mathematics. His texts-well known for their precision, readability, and pedagogical excellence-are used worldwide.

Affiliations and Expertise

(deceased) - Areas of Expertise: Analysis, Probability, and Statistics. Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, U.S.A. Please contact Gerardo Lafferriere at gerardolf@gmail.com for more information.

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