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Titlebook: Holomorphic Functions in the Plane and n-dimensional Space; Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig Textbook 2008 Birkhäuser Basel

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书目名称Holomorphic Functions in the Plane and n-dimensional Space
编辑Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig
视频videohttp://file.papertrans.cn/428/427953/427953.mp4
概述First textbook on elementary level introducing to classical complex analysis and its generalizations at the same time.Includes supplementary material:
图书封面Titlebook: Holomorphic Functions in the Plane and n-dimensional Space;  Klaus Gürlebeck,Klaus Habetha,Wolfgang Sprößig Textbook 2008 Birkhäuser Basel
描述.Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter..
出版日期Textbook 2008
关键词Clifford algebra; Clifford analysis; Complex analysis; holomorphic function; orthogonal decomposition
版次1
doihttps://doi.org/10.1007/978-3-7643-8272-8
isbn_softcover978-3-7643-8271-1
isbn_ebook978-3-7643-8272-8
copyrightBirkhäuser Basel 2008
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Klaus Gürlebeck,Klaus Habetha,Wolfgang SprößigFirst textbook on elementary level introducing to classical complex analysis and its generalizations at the same time.Includes supplementary material:
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978-3-7643-8271-1Birkhäuser Basel 2008
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Functions,We know already distances in ℂ, ℍ and .. They all have the following properties and define therefore a . in the respective sets: We have for a . .(., .) for all ., ., .:
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Integration and integral theorems,The Cauchy integral theorem belongs to the central results of complex analysis and tells us in its classical formulation that, for a holomorphic function . in a domain ., the integral along a sufficiently smooth closed curve which is located in . has always the value zero.
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Series expansions and local behavior,In this section we will use Cauchy’s integral theorem and the integral formula to derive results concerning the convergence behavior of function sequences.
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