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  • Textbook
  • © 2009

Analysis III

Birkhäuser
  • Numerous examples, real calculations, a large number of exercises and many figures make this book a reliable escort for the whole course of studies

  • Includes supplementary material: sn.pub/extras

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  • ISBN: 978-3-7643-7480-8
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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xii
  2. Integration theory

    Pages 59-231
  3. Integration on manifolds

    Pages 389-455
  4. Back Matter

    Pages 457-468

About this book

This third volume concludes our introduction to analysis, wherein we ?nish laying the groundwork needed for further study of the subject. As with the ?rst two, this volume contains more material than can treated in a single course. It is therefore important in preparing lectures to choose a suitable subset of its content; the remainder can be treated in seminars or left to independent study. For a quick overview of this content, consult the table of contents and the chapter introductions. Thisbookisalsosuitableasbackgroundforothercoursesorforselfstudy. We hope that its numerous glimpses into more advanced analysis will arouse curiosity and so invite students to further explore the beauty and scope of this branch of mathematics. In writing this volume, we counted on the invaluable help of friends, c- leagues, sta?, and students. Special thanks go to Georg Prokert, Pavol Quittner, Olivier Steiger, and Christoph Walker, who worked through the entire text cr- ically and so helped us remove errors and make substantial improvements. Our thanks also goes out to Carlheinz Kneisel and Bea Wollenmann, who likewise read the majority of the manuscript and pointed out various inconsistencies. Without the inestimable e?ortofour “typesetting perfectionist”, this volume could not have reached its present form: her tirelessness and patience with T X E and other software brought not only the end product, but also numerous previous versions,to a high degree of perfection. For this contribution, she has our greatest thanks.

Keywords

  • Analysis
  • Differential forms
  • Global analysis
  • Manifolds
  • Measure theory
  • calculus
  • differential equation
  • measure

Reviews

From the reviews:

“This third volume contains an introduction to Bochner-Lebesgue integral theory and differential forms’ calculus on smooth manifolds. … The text is clear and understandable and yet it provides a very detailed presentation of the covered topics from an advanced and abstract point of view. The reader can easily develop deep intuitive ideas following the numerous examples, exercises and pictures that are included.” (Tihomir Gyulov, Zentralblatt MATH, Vol. 1187, 2010)

Authors and Affiliations

  • Institut für Mathematik, Universität Zürich, Zürich, Switzerland

    Herbert Amann

  • Institut für Angewandte Mathematik, Universität Hannover, Hannover, Germany

    Joachim Escher

Bibliographic Information

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-3-7643-7480-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)