000 03005nam a22004335i 4500
001 978-3-0348-0180-5
003 DE-He213
005 20140220083253.0
007 cr nn 008mamaa
008 120828s2012 sz | s |||| 0|eng d
020 _a9783034801805
_9978-3-0348-0180-5
024 7 _a10.1007/978-3-0348-0180-5
_2doi
050 4 _aQA331-355
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.9
_223
100 1 _aWegert, Elias.
_eauthor.
245 1 0 _aVisual Complex Functions
_h[electronic resource] :
_bAn Introduction with Phase Portraits /
_cby Elias Wegert.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2012.
300 _aXIV, 360 p. 231 illus., 202 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- 1. Getting Acquainted -- 2. Complex Functions -- 3. Analytic Functions -- 4. Complex Calculus -- 5. Construction Principles -- 6. Conformal Mappings -- 7. Riemann Surfaces.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aFunctions of complex variables.
650 0 _aFunctions, special.
650 1 4 _aMathematics.
650 2 4 _aFunctions of a Complex Variable.
650 2 4 _aSpecial Functions.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034801799
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0180-5
912 _aZDB-2-SMA
999 _c101710
_d101710