LEADER 03262nam 22005175 450 001 9910254092203321 005 20211006151753.0 010 $a9783319421810 010 $a3319421816 024 7 $a10.1007/978-3-319-42181-0 035 $a(CKB)3710000000926147 035 $a(DE-He213)978-3-319-42181-0 035 $a(MiAaPQ)EBC5577735 035 $a(PPN)196325706 035 $a(MiAaPQ)EBC31851775 035 $a(Au-PeEL)EBL31851775 035 $a(OCoLC)1482814867 035 $a(EXLCZ)993710000000926147 100 $a20161026d2016 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Complex Analysis Problem Book /$fby Daniel Alpay 205 $a2nd ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2016. 215 $a1 online resource (X, 596 p.) 311 08$a9783319421797 311 08$a3319421794 320 $aIncludes bibliographical references and index. 327 $aPart I Complex Numbers -- Complex Numbers: Algebra -- Complex Numbers: Geometry -- Complex Numbers and Analysis -- Part II Functions of a Complex Variable -- Cauchy?Riemann Equations and C-differentiable Functions -- Cauchy?sTheorem -- Morera, Liouville, Schwarz, et les autres: First Applications -- Laurent Expansions, Residues, Singularities and Applications -- Computations of Definite Integrals Using the Residue Theorem -- Part III Applications and More Advanced Topics -- Harmonic Functions -- Conformal Mappings -- A Taste of Linear System Theory and Signal Processing -- Rational Functions -- Special Functions and Transforms -- Part IV Appendix -- Some Topology -- Some Functional Analysis Essentials -- A Brief Survey of Integration. 330 $aThis second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded. 606 $aFunctions of complex variables 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 615 0$aFunctions of complex variables. 615 14$aFunctions of a Complex Variable. 676 $a515.9 700 $aAlpay$b Daniel$4aut$4http://id.loc.gov/vocabulary/relators/aut$054298 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254092203321 996 $aComplex analysis problem book$91523047 997 $aUNINA