LEADER 04047nam 2200613 450 001 9910460278103321 005 20200520144314.0 010 $a1-118-70527-0 010 $a1-118-95639-7 035 $a(CKB)3710000000412056 035 $a(EBL)1895551 035 $a(SSID)ssj0001498631 035 $a(PQKBManifestationID)11799182 035 $a(PQKBTitleCode)TC0001498631 035 $a(PQKBWorkID)11505129 035 $a(PQKB)10626340 035 $a(MiAaPQ)EBC1895551 035 $a(DLC) 2014036105 035 $a(Au-PeEL)EBL1895551 035 $a(CaPaEBR)ebr11078102 035 $a(CaONFJC)MIL785546 035 $a(OCoLC)890377891 035 $a(EXLCZ)993710000000412056 100 $a20150725h20152015 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aComplex analysis $ea modern first course in function theory /$fJerry R. Muir, Jr 210 1$aHoboken, New Jersey :$cWiley,$d2015. 210 4$dİ2015 215 $a1 online resource (609 p.) 300 $aDescription based upon print version of record. 311 $a1-118-70522-X 320 $aIncludes bibliographical references and index. 327 $aCover; Table of Contents; Title Page; Copyright; Dedication; Preface; Chapter 1: The Complex Numbers; 1.1 Why?; 1.2 The Algebra of Complex Numbers; 1.3 The Geometry of the Complex Plane; 1.4 The Topology of the Complex Plane; 1.5 The Extended Complex Plane; 1.6 Complex Sequences; 1.7 Complex Series; Chapter 2: Complex Functions and Mappings; 2.1 Continuous Functions; 2.2 Uniform Convergence; 2.3 Power Series; 2.4 Elementary Functions and Euler's Formula; 2.5 Continuous Functions as Mappings; 2.6 Linear Fractional Transformations; 2.7 Derivatives; 2.8 The Calculus of Real-Variable Functions 327 $a2.9 Contour Integrals Chapter 3: Analytic Functions; 3.1 The Principle of Analyticity; 3.2 Differentiable Functions are Analytic; 3.3 Consequences of Goursat's Theorem; 3.4 The Zeros of Analytic Functions; 3.5 The Open Mapping Theorem and Maximum Principle; 3.6 The Cauchy-Riemann Equations; 3.7 Conformal Mapping and Local Univalence; Chapter 4: Cauchy's Integral Theory; 4.1 The Index of a Closed Contour; 4.2 The Cauchy Integral Formula; 4.3 Cauchy's Theorem; Chapter 5: The Residue Theorem; 5.1 Laurent Series; 5.2 Classification of Singularities; 5.3 Residues; 5.4 Evaluation of Real Integrals 327 $a5.5 The Laplace Transform Chapter 6: Harmonic Functions and Fourier Series; 6.1 Harmonic Functions; 6.2 The Poisson Integral Formula; 6.3 Further Connections to Analytic Functions; 6.4 Fourier Series; Epilogue; Local Uniform Convergence; Harnack's Theorem; Results for Simply Connected Domains; The Riemann Mapping Theorem; Appendix A: Sets and Functions; Sets and Elements; Functions; Appendix B: Topics from Advanced Calculus; The Supremum and Infimum; Uniform Continuity; The Cauchy Product; Leibniz's Rule; References; Index; End User License Agreement 330 $aA thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic fun 606 $aGeometric function theory 606 $aNumbers, Complex 608 $aElectronic books. 615 0$aGeometric function theory. 615 0$aNumbers, Complex. 676 $a515 700 $aMuir$b Jerry R.$f1973-$0969742 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910460278103321 996 $aComplex analysis$92203713 997 $aUNINA