التحليل Analysis III

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Analysis

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Analysis I​


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By Herbert Amann, Joachim Escher "Analysis I "
Publisher: Birkhäuser Basel | Pages: 426 | 2005 | ISBN: 3764371536 | PDF | 2MB​

Book Description:​

This book is the first of a three volume introduction to analysis. It is distinguished by its modern and clear presentation, concentrating always on the essential concepts. In contrast to most other textbooks, there is no artificial separation between the theories of one variable and that of many variables. Emphasis is placed on the early development of a solid foundation in topology. As well, the basics of complex analysis are covered.​

This book is directed primarily to the students and instructors of beginning courses in analysis. But, with the many examples, exercises and the supplementary material, it is also suitable for self-study, as preparation for advanced study, and as a basis for other research in mathematics and physics.​


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Analysis II​

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Herbert Amann, Joachim Escher “Analysis II"
Birkhäuser Basel | 2008 | ISBN: 3764374721 | 400 pages | PDF | 3,2 MB ​

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 (3-7643-7153-6) continues. In this way a sustainable basis will be created which allows to deal with interesting applications that sometimes go considerably beyond the material that is 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. Another example is the presentation of the local theory of submanifolds of Rn.​



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Analysis III​


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Herbert Amann, Joachim Escher, "Analysis III"
Birkhäuser Basel | 2009 | ISBN: 3764374799 | 468 pages | PDF | 10 MB ​

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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