MARC Record from marc_columbia

LEADER: 05295fam a2200397 a 4500
001 1686740
005 20220608212403.0
008 920526t19931993nyua b 001 0 eng
010 $a 92021625
020 $a0387978860 (New York : acid-free paper)
020 $a3540978860 (Berlin : acid-free paper)
035 $a(OCoLC)26013113
035 $a(OCoLC)ocm26013113
035 $9AKV6652CU
035 $a(NNC)1686740
035 $a1686740
040 $aDLC$cDLC$dDLC$dOrLoB
050 00 $aQA331.7$b.L36 1993
082 00 $a515/.9$220
100 1 $aLang, Serge,$d1927-2005.$0http://id.loc.gov/authorities/names/n79053939
245 10 $aComplex analysis /$cSerge Lang.
250 $a3rd ed.
260 $aNew York :$bSpringer-Verlag,$c[1993], ©1993.
300 $axiv, 458 pages :$billustrations ;$c25 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aGraduate texts in mathematics ;$v103
504 $aIncludes bibliographical references (p. [454]) and index.
505 00 $gPt. 1.$tBasic Theory.$gCh. I.$tComplex Numbers and Functions.$g1.$tDefinition.$g2.$tPolar Form.$g3.$tComplex Valued Functions.$g4.$tLimits and Compact Sets.$tCompact Sets.$g5.$tComplex Differentiability.$g6.$tThe Cauchy-Riemann Equations.$g7.$tAngles Under Holomorphic Maps.$gCh. II.$tPower Series.$g1.$tFormal Power Series.$g2.$tConvergent Power Series.$g3.$tRelations Between Formal and Convergent Series.$tSums and Products.$tQuotients.$tComposition of Series.$g4.$tAnalytic Functions.$g5.$tDifferentiation of Power Series.$g6.$tThe Inverse and Open Mapping Theorems.$g7.$tThe Local Maximum Modulus Principle.$gCh. III.$tCauchy's Theorem, First Part.$g1.$tHolomorphic Functions on Connected Sets.$tAppendix: Connectedness.$g2.$tIntegrals Over Paths.$g3.$tLocal Primitive for a Holomorphic Function.$g4.$tAnother Description of the Integral Along a Path.$g5.$tThe Homotopy Form of Cauchy's Theorem.$g6.$tExistence of Global Primitives. Definition of the Logarithm.$g7.$tThe Local Cauchy Formula.
505 80 $gCh. IV.$tWinding Numbers and Cauchy's Theorem.$g1.$tThe Winding Number.$g2.$tThe Global Cauchy Theorem.$tDixon's Proof of Theorem 2.5 (Cauchy's Formula).$g3.$tArtin's Proof.$gCh. V.$tApplications of Cauchy's Integral Formula.$g1.$tUniform Limits of Analytic Functions.$g2.$tLaurent Series.$g3.$tIsolated Singularities.$tRemovable Singularities.$tPoles.$tEssential Singularities.$gCh. VI.$tCalculus of Residues.$g1.$tThe Residue Formula.$tResidues of Differentials.$g2.$tEvaluation of Definite Integrals.$tFourier Transforms.$tTrigonometric Integrals.$tMellin Transforms.$gCh. VII.$tConformal Mappings.$g1.$tSchwarz Lemma.$g2.$tAnalytic Automorphisms of the Disc.$g3.$tThe Upper Half Plane.$g4.$tOther Examples.$g5.$tFractional Linear Transformations.$gCh. VIII.$tHarmonic Functions.$g1.$tDefinition.$tApplication: Perpendicularity.$tApplication: Flow Lines.$g2.$tExamples.$g3.$tBasic Properties of Harmonic Functions.$g4.$tThe Poisson Formula.$g5.$tConstruction of Harmonic Functions --
505 80 $gPt. 2.$tGeometric Function Theory.$gCh. IX.$tSchwarz Reflection.$g1.$tSchwarz Reflection (by Complex Conjugation).$g2.$tReflection Across Analytic Arcs.$g3.$tApplication of Schwarz Reflection.$gCh. X.$tThe Riemann Mapping Theorem.$g1.$tStatement of the Theorem.$g2.$tCompact Sets in Function Spaces.$g3.$tProof of the Riemann Mapping Theorem.$g4.$tBehavior at the Boundary.$gCh. XI.$tAnalytic Continuation Along Curves.$g1.$tContinuation Along a Curve.$g2.$tThe Dilogarithm.$g3.$tApplication to Picard's Theorem --$gPt. 3.$tVarious Analytic Topics.$gCh. XII.$tApplications of the Maximum Modulus Principle and Jensen's Formula.$g1.$tJensen's Formula.$g2.$tThe Picard-Borel Theorem.$g3.$tBounds by the Real Part, Borel-Caratheodory Theorem.$g4.$tThe Use of Three Circles and the Effect of Small Derivatives.$tHermite Interpolation Formula.$g5.$tEntire Functions with Rational Values.$g6.$tThe Phragmen-Lindelof and Hadamard Theorems.$gCh. XIII.$tEntire and Meromorphic Functions.$g1.$tInfinite Products.
505 80 $g2.$tWeierstrass Products.$g3.$tFunctions of Finite Order.$g4.$tMeromorphic Functions, Mittag-Leffler Theorem.$gCh. XIV.$tElliptic Functions.$g1.$tThe Liouville Theorems.$g2.$tThe Weierstrass Function.$g3.$tThe Addition Theorem.$g4.$tThe Sigma and Zeta Functions.$gCh. XV.$tThe Gamma and Zeta Functions.$g1.$tThe Differentiation Lemma.$g2.$tThe Gamma Function.$tWeierstrass Product.$tThe Mellin Transform.$tProof of Stirling's Formula.$g3.$tThe Lerch Formula.$g4.$tZeta Functions.$gCh. XVI.$tThe Prime Number Theorem.$g1.$tBasic Analytic Properties of the Zeta Function.$g2.$tThe Main Lemma and its Application.$g3.$tProof of the Main Lemma.$tApp. 1. Summation by Parts and Non-Absolute Convergence --$tApp. 2. Difference Equations --$tApp. 3. Analytic Differential Equations --$tApp. 4. Fixed Points of a Fractional Linear Transformation --$tApp. 5. Cauchy's Formula for C[actual symbol not reproducible] Functions.
650 0 $aFunctions of complex variables.$0http://id.loc.gov/authorities/subjects/sh85052356
650 0 $aMathematical analysis.$0http://id.loc.gov/authorities/subjects/sh85082116
830 0 $aGraduate texts in mathematics ;$v103.$0http://id.loc.gov/authorities/names/n83723435
852 00 $bmat$hQA331.7$i.L36 1993