A Course in Real Analysis

ISBN-13: 9780123877741 / Angielski / Twarda / 2012 / 667 str.

Neil A. Weiss; John McDonald

Opis

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.

• 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

Recenzje

"...truly marvelous...weaves an interesting, lively, and crystal clear sequence of ideas comprising the heart of modern analysis. The order of presentation is so carefully chosen and the exposition is so masterful as to possess the traits of a literary art form." --MAA Reviews, January 2015

"The exposition is very clear and unhurried and the book would be useful both as a text and a book for self-study. The last chapters go beyond what is usually covered in analysis courses and this is all to the good." --Sigurdur Helgason, MIT

"There is a literary quality in the writing that is rare in mathematics texts. It is a pleasure to read this book. The exercises are a strong feature of the book and the examples are well chosen and plentiful." --Peter Duren, University of Michigan

"The outstanding features of the book are the wealth of examples and exercises, the interesting biographical data, and the introduction to wavelets and dynamical systems." --Duong H. Phong, Columbia University

"McDonald and Weiss have crafted a treasure chest of exercises in real analysis. Just an amazing and broad collection. Students and researchers will surely benefit from the enormous amount of superb exercises." --Enno Lenzmann, University of Copenhagen

"I was very impressed by the motivating discussions of a number of difficult concepts, along with their fresh approach to the details following. Their general philosophy of starting with concrete ideas, and slowly abstracting, worked well in communicating even the most difficult concepts in the course." --Todd Kemp, University of California, San Diego

Spis treści

1. Set Theory2. The Real Number System and Calculus3. Lebesgue Measure on the Real Line4. The Lebesgue Integral on the Real Line5. Elements of Measure Theory6. Extensions to Measures and Product Measure7. Elements of Probability8. Differentiation and Absolute Continuity9. Signed and Complex Measures10. Topologies, Metrics, and Norms11. Separability and Compactness12. Complete and Compact Spaces13. Hilbert Spaces and Banach Spaces14. Normed Spaces and Locally Convex Spaces15. Elements of Harmonic Analysis16. Measurable Dynamical Systems17. Hausdorff Measure and Fractals

O autorze

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.