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Kurzbeschreibung
An in-depth look at real analysis and its applications-now expanded and revised.
This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.
This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include:
* Revised material on the n-dimensional Lebesgue integral.
* An improved proof of Tychonoff's theorem.
* Expanded material on Fourier analysis.
* A newly written chapter devoted to distributions and differential equations.
* Updated material on Hausdorff dimension and fractal dimension.
This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.
This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include:
* Revised material on the n-dimensional Lebesgue integral.
* An improved proof of Tychonoff's theorem.
* Expanded material on Fourier analysis.
* A newly written chapter devoted to distributions and differential equations.
* Updated material on Hausdorff dimension and fractal dimension.
Synopsis
An in-depth look at real analysis and its applications-now expanded and revised. This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory. This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include: Revised material on the n-dimensional Lebesgue integral. An improved proof of Tychonoff's theorem. Expanded material on Fourier analysis.A newly written chapter devoted to distributions and differential equations. Updated material on Hausdorff dimension and fractal dimension.
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Die hilfreichsten Kundenrezensionen
1 von 1 Kunden fanden die folgende Rezension hilfreich:
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Great book,
Rezension bezieht sich auf: Real Analysis: Modern Techniques and Their Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monog) (Gebundene Ausgabe)
What I like most about the book is its concise but broad coverage of the fundamentals of real and functional analysis. Although I am not a mathematician, my main interest is solving various engineering problems using numerical methods. A solid background in real and functional analysis would be necessary for deeper understanding of various numerical methods. I wish I had known this book the first time I felt the need to study basic modern analysis. This books has exactly the material I wanted to learn.In addition to the theorems and proofs, the author tells you why some theorems are important and how they can be used (of course also in a concise way). I found this type of "hints" are extremely helpful. The historical notes at the end of each chapter are also interesting to read. Helfen Sie anderen Kunden bei der Suche nach den hilfreichsten Rezensionen
1 von 1 Kunden fanden die folgende Rezension hilfreich:
5.0 von 5 Sternen
Stellar!!Very demanding,but well worth the effort.,
Von Ein Kunde
Rezension bezieht sich auf: Real Analysis: Modern Techniques and Their Applications (Pure and Applied Math (Wiley)) (Gebundene Ausgabe)
Folland's book is extremely terse, but very elegant. It covers topics in great generality. I haven't read the whole book,but the parts I read were excellent. Its a damned hard book, but very precise and conveys a great deal of information. Its certainly not easy reading, it makes the reader (at least it made me) think quite a bit since the proofs are very terse. I think that the amount learned is certainly worth the effort. A classic and one that I would definitely recommend!
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