02914nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100002900207245012500236260008200361300003400443336002600477337002600503338003600529347002400565490003900589506006600628520160800694650002902302650004102331650005502372700002802427856003202455856006502487164-130506CH-001817-320130506234500.0a fot ||| 0|cr nn mmmmamaa130506e20130506sz fot ||| 0|eng d a978303719611370a10.4171/1112doi ach0018173 7aPBKD2bicssc a30-xxa32-xx2msc1 aBruna, Joaquim,eauthor.10aComplex Analysish[electronic resource] :bTranslated from the Catalan by Ignacio Monreal /cJoaquim Bruna, Julià Cufí3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2013 a1 online resource (576 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Textbooks in Mathematics (ETB)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php 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.07aComplex analysis2bicssc07aFunctions of a complex variable2msc07aSeveral complex variables and analytic spaces2msc1 aCufí, Julià,eauthor.40uhttps://doi.org/10.4171/111423cover imageuhttps://www.ems-ph.org/img/books/bruna_mini.jpg