000			03106nam a22004095a 4500
001			164-130506
003			CH-001817-3
005			20170613140814.0
006			a fot ||| 0|
007			cr nn mmmmamaa
008			130506e20130506sz fot ||| 0|eng d
020			_a9783037196113
024	7	0	_a10.4171/111 _2doi
040			_ach0018173
072		7	_aPBKD _2bicssc
084			_a30-xx _a32-xx _2msc
100	1		_aBruna, Joaquim, _eauthor.
245	1	0	_aComplex Analysis _h[electronic resource] : _bTranslated from the Catalan by Ignacio Monreal / _cJoaquim Bruna, Julià Cufí
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2013
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2013
300			_a1 online resource (576 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	0		_aEMS Textbooks in Mathematics (ETB)
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
520			_aThe theory of functions of a complex variable is a central theme in mathematical analysis that has links to several branches of mathematics. Understanding the basics of the theory is necessary for anyone who wants to have a general mathematical training or for anyone who wants to use mathematics in applied sciences or technology. The book presents the basic theory of analytic functions of a complex variable and their points of contact with other parts of mathematical analysis. This results in some new approaches to a number of topics when compared to the current literature on the subject. Some issues covered are: a real version of the Cauchy–Goursat theorem, theorems of vector analysis with weak regularity assumptions, an approach to the concept of holomorphic functions of real variables, Green’s formula with multiplicities, Cauchy’s theorem for locally exact forms, a study in parallel of Poisson’s equation and the inhomogeneous Cauchy–Riemann equations, the relationship between Green’s function and conformal mapping, the connection between the solution of Poisson’s equation and zeros of holomorphic functions, and the Whittaker–Shannon theorem of information theory. The text can be used as a manual for complex variable courses of various levels and as a reference book. The only prerequisites for reading it is a working knowledge of the topology of the plane and the differential calculus for functions of several real variables. A detailed treatment of harmonic functions also makes the book useful as an introduction to potential theory.
650	0	7	_aComplex analysis _2bicssc
650	0	7	_aFunctions of a complex variable _2msc
650	0	7	_aSeveral complex variables and analytic spaces _2msc
700	1		_aBruna, Joaquim, _eauthor.
700	1		_aCufí, Julià, _eauthor.
856	4	0	_uhttps://doi.org/10.4171/111
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/bruna_mini.jpg
942			_2EBK13834 _cEBK
999			_c50458 _d50458