Analysis  1 ~ 3

Herbert Amann, Joachim Escher

The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and clear development that started in Volume I is continued. In this way a sustainable basis is created which allows the reader to deal with interesting applications that sometimes go beyond material represented in traditional textbooks. This applies, for instance, to the exploration of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations.

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The third and last volume of this work is devoted to integration theory and the fundamentals of global analysis. Once again, emphasis is laid on a modern and clear organization, leading to a well structured and elegant theory and providing the reader with effective means for further development. Thus, for instance, the Bochner-Lebesgue integral is considered with care, since it constitutes an indispensable tool in the modern theory of partial differential equations. Similarly, there is discussion and a proof of a version of Stokes' Theorem that makes ample allowance for the practical needs of mathematicians and theoretical physicists. As in earlier volumes, there are many glimpses of more advanced topics, which serve to give the reader an idea of the importance and power of the theory. These prospective sections also help drill in and clarify the material presented. Numerous examples, concrete calculations, a variety of exercises and a generous number of illustrations make this textbook a reliable guide and companion for the study of analysis.

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"This textbook provides an outstanding introduction to analysis. It is distinguished by its high level of presentation and its focus on the essential." (Zeitschrift fur Analysis und ihre Anwendung 18, No. 4 - G. Berger, review of the first German edition) "One advantage of this presentation is that the power of the abstract concepts are convincingly demonstrated using concrete applications." (W. Grolz, review of the first German edition)

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[目次]

  • Elements of measure theory.- Integration theory.- Manifolds and differential forms.- Integration on manifolds.

「Nielsen BookData」より

[目次]

  • Integral calculus in one variable.- Multivariable differential calculus.- Line integrals.

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[目次]

  • Foundations.- Convergence.- Continuous Functions.- Differentiation in One Variable.- Sequences of Functions.

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この本の情報

書名 Analysis
著作者等 Amann, H.
Amann H.
Amann Herbert
Escher Joachim
巻冊次 1
2
3
出版元 Birkhäuser
刊行年月 c2005-c2009
ページ数 3 v.
大きさ 25 cm
ISBN 3764371536
0817671536
9783764374792
9783764374723
NCID BA69905039
※クリックでCiNii Booksを表示
言語 英語
原文言語 ドイツ語
出版国 スイス
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