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Analysis II

  • Book
  • © 2008

Overview

Authors:
  1. Herbert Amann

    1. Institut für Mathematik, Universität Zürich, Zürich, Switzerland

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  2. Joachim Escher

    1. Institut für Angewandte Mathematik, Universität Hannover, Hannover, Germany

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    You can also search for this author in PubMed   Google Scholar

  • Cauchy’s integral theorems and the theory of holomorphic functions including the homological version of the residue theorem are derived as an application of the theory of line integrals
  • In addition to the calculation of important definite integrals which appear in Mathematics and in Physics, theoretic properties of the Gamma function and Riemann’s Zeta function are explored
  • Numerous examples with varying degrees of difficulty and many informative figures
  • Includes supplementary material: sn.pub/extras

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-xii
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  2. Integral calculus in one variable

    Pages 1-113

  3. Multivariable differential calculus

    Pages 115-278

  4. Line integrals

    Pages 279-385

  5. Back Matter

    Pages 387-400
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About this book

As with the first, the second volume contains substantially more material than can be covered in a one-semester course. Such courses may omit many beautiful and well-grounded applications which connect broadly to many areas of mathematics. We of course hope that students will pursue this material independently; teachers may find it useful for undergraduate seminars. For an overview of the material presented, consult the table of contents and the chapter introductions. As before, we stress that doing the numerous exercises is indispensable for understanding the subject matter, and they also round out and amplify the main text. In writing this volume, we are indebted to the help of many. We especially thank our friends and colleagues Pavol Quittner and Gieri Simonett. They have not only meticulously reviewed the entire manuscript and assisted in weeding out errors but also, through their valuable suggestions for improvement, contributed essentially to the final version. We also extend great thanks to our staff for their careful perusal of the entire manuscript and for tracking errata and inaccuracies. Our most heartfelt thank extends again to our “typesetting perfectionist”, 1 without whose tireless effort this book would not look nearly so nice. We also thank Andreas for helping resolve hardware and software problems. Finally, we extend thanks to Thomas Hintermann and to Birkhauser for the good working relationship and their understanding of our desired deadlines.

Authors and Affiliations

  • Institut für Mathematik, Universität Zürich, Zürich, Switzerland

    Herbert Amann

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

    Joachim Escher

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