Analysis
著者
書誌事項
Analysis
Birkhäuser, c2005-c2009
- 1
- 1
- 2
- 3
- 統一タイトル
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Analysis I
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注記
Includes bibliographical references and index
Translated from the German by Gary Brokfield
2-3: Translated from the German by Silvio Levy and Matthew Cargo
Originally published in German under the same title by Birkhäuser Verlag, Switzerland
内容説明・目次
- 巻冊次
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1 ISBN 9783764371531
内容説明
"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. Groelz, review of the first German edition)
目次
Foundations.- Convergence.- Continuous Functions.- Differentiation in One Variable.- Sequences of Functions.
- 巻冊次
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2 ISBN 9783764374723
内容説明
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.
目次
Integral calculus in one variable.- Multivariable differential calculus.- Line integrals.
- 巻冊次
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3 ISBN 9783764374792
内容説明
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.
目次
Elements of measure theory.- Integration theory.- Manifolds and differential forms.- Integration on manifolds.
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