05397nam 2200769 n 450 991097100150332120251117110653.01-383-02422-70-19-103720-60-19-158333-210.1093/oso/9780198525615.001.0001(CKB)2670000000545495(EBL)1657778(SSID)ssj0001216221(PQKBManifestationID)11704111(PQKBTitleCode)TC0001216221(PQKBWorkID)11190870(PQKB)10817188(Au-PeEL)EBL1657778(CaPaEBR)ebr10851001(CaONFJC)MIL584413(OCoLC)875098009(Au-PeEL)EBL7034662(MiAaPQ)EBC1657778(OCoLC)1406782114(StDuBDS)9781383024227(MiAaPQ)EBC7034662(OCoLC)874563358(EXLCZ)99267000000054549520040119e20232003 |y |engur|n|---|||||txtccrIntroduction to complex analysis /H.A. PriestleySecond edition.Oxford :Oxford University Press,2023.1 online resource (343 p.)Oxford scholarship onlinePrevious edition: Oxford : Clarendon, 1990.Previously issued in print: 2003.0-19-852561-3 0-19-852562-1 Includes bibliographical references and index.Cover; 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; Möbius 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 functionsDifferentiation 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 mappingsExercises9. 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; Exercises14. 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 theoremCalculation 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 transformBasic properties and evaluation of Laplace transformsThis 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.Oxford scholarship online.Mathematical analysisFunctions of complex variablesMathematical analysis.Functions of complex variables.515.9Priestley H. A(Hilary A.),246852StDuBDSUkStDuBDSZStDuBDSZBOOK9910971001503321Introduction to complex analysis622573UNINA