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Basic Real Analysis
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Basic Real Analysis

Basic Real Analysis

Anthony W. Knapp - Collection Cornerstones

670 pages, parution le 15/01/2005

Résumé

Basic Real Analysis and Advanced Real Analysis systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.

Key topics and features of Basic Real Analysis:

  • Early chapters treat the fundamentals of real variables, sequences and series of functions, the theory of Fourier series for the Riemann integral, metric spaces, and the theoretical underpinnings of multivariable calculus and differential equations
  • Subsequent chapters develop the Lebesgue theory in Euclidean and abstract spaces, Fourier series and the Fourier transform for the Lebesgue integral, point-set topology, measure theory in locally compact Hausdorff spaces, and the basics of Hilbert and Banach spaces
  • The subjects of Fourier series and harmonic functions are used as recurring motivation for a number of theoretical developments
  • The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them
  • The text includes many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most of the problems

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 students preparing 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.

Written for: Advanced undergraduates, graduate students, pure and applied mathematicians working in analytic areas such as statisitics, math physics, electrical engineering, and differential equations

Sommaire

  • Dependence among Chapters
  • Guide for the Reader
  • List of Figures
  • Acknowledgements
  • Standard Notation
  • Theory of Calculus in One Real Variable
  • Metric Spaces
  • Theory of Calculus in Several Real Variables
  • Theory of Ordinary Differential Equations
  • Abstract Measure Theory and Lebesgue Measure
  • Measure Theory for Euclidean Space
  • Differentiation of Lebesgue Integrals on the Line
  • Fourier Transform in Euclidean Space
  • Lp Spaces
  • Topological Spaces
  • Integration of Locally Compact Spaces
  • Hilbert and Banach Spaces
  • Appendix
  • Hints for Solutions of Problems
  • Selected References
  • Index of Notation
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Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Anthony W. Knapp
Collection Cornerstones
Parution 15/01/2005
Nb. de pages 670
Format 16 x 24
Couverture Relié
Poids 1060g
Intérieur Noir et Blanc
EAN13 9780817632502
ISBN13 978-0-8176-3250-2

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