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＜電子ブック＞
Visual Complex Functions : An Introduction with Phase Portraits / by Elias Wegert

版	1st ed. 2012.
出版者	(Basel : Springer Basel : Imprint: Birkhäuser)
出版年	2012
大きさ	XIV, 360 p. 231 illus., 202 illus. in color : online resource
著者標目	*Wegert, Elias author SpringerLink (Online service)
件　名	LCSH:Functions of complex variables LCSH:Special functions FREE:Functions of a Complex Variable FREE:Special Functions
一般注記	Preface -- 1. Getting Acquainted -- 2. Complex Functions -- 3. Analytic Functions -- 4. Complex Calculus -- 5. Construction Principles -- 6. Conformal Mappings -- 7. Riemann Surfaces This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains. Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits HTTP:URL=https://doi.org/10.1007/978-3-0348-0180-5

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