LEADER 05407nam 2200673 450 001 9910787994303321 005 20230328222707.0 010 $a1-383-02422-7 010 $a0-19-103720-6 010 $a0-19-158333-2 035 $a(CKB)2670000000545495 035 $a(EBL)1657778 035 $a(SSID)ssj0001216221 035 $a(PQKBManifestationID)11704111 035 $a(PQKBTitleCode)TC0001216221 035 $a(PQKBWorkID)11190870 035 $a(PQKB)10817188 035 $a(Au-PeEL)EBL1657778 035 $a(CaPaEBR)ebr10851001 035 $a(CaONFJC)MIL584413 035 $a(OCoLC)875098009 035 $a(Au-PeEL)EBL7034662 035 $a(MiAaPQ)EBC1657778 035 $a(EXLCZ)992670000000545495 100 $a20140402e20052003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to complex analysis /$fH. A. Priestley 205 $aSecond edition. 210 1$aOxford, England :$cOxford University Press,$d2005. 210 4$dİ2003 215 $a1 online resource (343 p.) 300 $aDescription based upon print version of record. 311 $a0-19-852561-3 311 $a0-19-852562-1 320 $aIncludes bibliographical references and index. 327 $aCover; Contents; Notation and terminology; 1. The complex plane; Complex numbers; Algebra in the complex plane; Conjugation, modulus, and inequalities; Exercises; 2. Geometry in the complex plane; Lines and circles; The extended complex plane and the Riemann sphere; Mo?bius transformations; Exercises; 3. Topology and analysis in the complex plane; Open sets and closed sets in the complex plane; Convexity and connectedness; Limits and continuity; Exercises; 4. Paths; Introducing curves and paths; Properties of paths and contours; Exercises; 5. Holomorphic functions 327 $aDifferentiation and the Cauchy-Riemann equationsHolomorphic functions; Exercises; 6. Complex series and power series; Complex series; Power series; A proof of the Differentiation theorem for power series; Exercises; 7. A cornucopia of holomorphic functions; The exponential function; Complex trigonometric and hyperbolic functions; Zeros and periodicity; Argument, logarithms, and powers; Holomorphic branches of some simple multifunctions; Exercises; 8. Conformal mapping; Conformal mapping; Some standard conformal mappings; Mappings of regions by standard mappings; Building conformal mappings 327 $aExercises9. Multifunctions; Branch points and multibranches; Cuts and holomorphic branches; Exercises; 10. Integration in the complex plane; Integration along paths; The Fundamental theorem of calculus; Exercises; 11. Cauchy's theorem: basic track; Cauchy's theorem; Deformation; Logarithms again; Exercises; 12. Cauchy's theorem: advanced track; Deformation and homotopy; Holomorphic functions in simply connected regions; Argument and index; Cauchy's theorem revisited; Exercises; 13. Cauchy's formulae; Cauchy's integral formula; Higher-order derivatives; Exercises 327 $a14. Power series representationIntegration of series in general and power series in particular; Taylor's theorem; Multiplication of power series; A primer on uniform convergence; Exercises; 15. Zeros of holomorphic functions; Characterizing zeros; The Identity theorem and the Uniqueness theorem; Counting zeros; Exercises; 16. Holomorphic functions: further theory; The Maximum modulus theorem; Holomorphic mappings; Exercises; 17. Singularities; Laurent's theorem; Singularities; Meromorphic functions; Exercises; 18. Cauchy's residue theorem; Residues and Cauchy's residue theorem 327 $aCalculation of residuesExercises; 19. A technical toolkit for contour integration; Evaluating real integrals by contour integration; Inequalities and limits; Estimation techniques; Improper and principal-value integrals; Exercises; 20. Applications of contour integration; Integrals of rational functions; Integrals of other functions with a finite number of poles; Integrals involving functions with infinitely many poles; Integrals involving multifunctions; Evaluation of definite integrals: overview (basic track); Summation of series; Further techniques; Exercises; 21. The Laplace transform 327 $aBasic properties and evaluation of Laplace transforms 330 $aComplex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have beensubstantially revised and enlarged, with carefully graded exercises at the end of each chapter.This is the latest additi 606 $aMathematical analysis 606 $aFunctions of complex variables 615 0$aMathematical analysis. 615 0$aFunctions of complex variables. 676 $a515.9 700 $aPriestley$b H. A$g(Hilary A.),$0246852 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910787994303321 996 $aIntroduction to complex analysis$9622573 997 $aUNINA