LEADER 05397nam 2200769 n 450 001 9910971001503321 005 20251117110653.0 010 $a1-383-02422-7 010 $a0-19-103720-6 010 $a0-19-158333-2 024 7 $a10.1093/oso/9780198525615.001.0001 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(OCoLC)1406782114 035 $a(StDuBDS)9781383024227 035 $a(MiAaPQ)EBC7034662 035 $a(OCoLC)874563358 035 $a(EXLCZ)992670000000545495 100 $a20040119e20232003 |y | 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 :$cOxford University Press,$d2023. 215 $a1 online resource (343 p.) 225 1 $aOxford scholarship online 300 $aPrevious edition: Oxford : Clarendon, 1990. 300 $aPreviously issued in print: 2003. 311 08$a0-19-852561-3 311 08$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 8 $aThis second edition of Priestley's well-known text is aimed at students taking an introductory core course in Complex Analysis, a classical and central area of mathematics. Graded exercises are presented throughout the text along with worked examples on the more elementary topics. 410 0$aOxford scholarship online. 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.),$0246852 801 0$bStDuBDS 801 2$bUk 801 2$bStDuBDSZ 801 2$bStDuBDSZ 906 $aBOOK 912 $a9910971001503321 996 $aIntroduction to complex analysis$9622573 997 $aUNINA