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Analysis I

作者：Herbert Amann

出版社：Birkhäuser

出版年：2005-2-14

评分：9.7

ISBN：9783764371531

所属分类：行业好书

书刊介绍

内容简介

Logical thinking, the analysis of complex relationships, the recognition of und- lying simple structures which are common to a multitude of problems — these are the skills which are needed to do mathematics, and their development is the main goal of mathematics education. Of course, these skills cannot be learned ‘in a vacuum’. Only a continuous struggle with concrete problems and a striving for deep understanding leads to success. A good measure of abstraction is needed to allow one to concentrate on the essential, without being distracted by appearances and irrelevancies. The present book strives for clarity and transparency. Right from the beg- ning, it requires from the reader a willingness to deal with abstract concepts, as well as a considerable measure of self-initiative. For these e?orts, the reader will be richly rewarded in his or her mathematical thinking abilities, and will possess the foundation needed for a deeper penetration into mathematics and its applications. Thisbookisthe?rstvolumeofathreevolumeintroductiontoanalysis.It- veloped from courses that the authors have taught over the last twenty six years at theUniversitiesofBochum,Kiel,Zurich,BaselandKassel.Sincewehopethatthis book will be used also for self-study and supplementary reading, we have included far more material than can be covered in a three semester sequence. This allows us to provide a wide overview of the subject and to present the many beautiful and important applications of the theory. We also demonstrate that mathematics possesses, not only elegance and inner beauty, but also provides e?cient methods for the solution of concrete problems.

作品目录

Front Matter
Pages i-xv
Foundations
Pages 1-128
Convergence
Pages 129-216
Continuous Functions
Pages 217-298
Differentiation in One Variable
Pages 299-359
Sequences of Functions
Pages 361-403
Back Matter
Pages 405-430
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