000 02627nam a22004095i 4500
001 978-3-0348-0078-5
003 DE-He213
005 20140220083739.0
007 cr nn 008mamaa
008 110818s2011 sz | s |||| 0|eng d
020 _a9783034800785
_9978-3-0348-0078-5
024 7 _a10.1007/978-3-0348-0078-5
_2doi
050 4 _aQA331-355
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.9
_223
100 1 _aAlpay, Daniel.
_eauthor.
245 1 2 _aA Complex Analysis Problem Book
_h[electronic resource] /
_cby Daniel Alpay.
264 1 _aBasel :
_bSpringer Basel,
_c2011.
300 _aX, 526p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPrologue -- I Complex numbers -- 1 Complex numbers: algebra -- 2 Complex numbers: geometry -- 3 Complex numbers and analysis -- 4. Remarks and generalizations: quaternions, etc -- II Functions of a complex variable -- 5 C-differentiable functions -- 6 Cauchy's theorem -- 7 First applications -- 8 Laurent expansions and applications -- 9 Computations of definite integrals -- 10 Harmonic functions -- 11 Conformal mappings.-III Complements -- 12 Some useful theorems -- 13 Some topology -- References -- Index.
520 _aThis is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises show the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of  important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.
650 0 _aMathematics.
650 0 _aFunctions of complex variables.
650 1 4 _aMathematics.
650 2 4 _aFunctions of a Complex Variable.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034800778
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0078-5
912 _aZDB-2-SMA
999 _c106589
_d106589