LEADER 00906cam0-22003131i-450- 001 990006773770403321 005 20121121092623.0 035 $a000677377 035 $aFED01000677377 035 $a(Aleph)000677377FED01 035 $a000677377 100 $a20010426d1993----km-y0itay50------ba 101 0 $aita 102 $aIT 105 $ay-------001yy 200 1 $a<>frode fiscale$eprofili sistematici delle disposizioni penali dell'art. 4 legge 516/82$fFabrizio Lemme 205 $a3. ed. riv. ed agg. 210 $aNapoli$cJovene$d1993 215 $a180 p.$d24 cm 610 0 $aReati fiscali$aGiurisprudenza 676 $a345.45023$v19$zita 700 1$aLemme,$bFabrizio$f<1936- >$0216528 801 0$aIT$bUNINA$gREICAT$2UNIMARC 901 $aBK 912 $a990006773770403321 952 $aV B 160$b20745$fFSPBC 959 $aFSPBC 996 $aFrode fiscale$9270379 997 $aUNINA LEADER 05501nam 22005055 450 001 9910480773503321 005 20200630082638.0 010 $a1-4612-1534-X 024 7 $a10.1007/978-1-4612-1534-9 035 $a(CKB)3400000000089589 035 $a(SSID)ssj0000808068 035 $a(PQKBManifestationID)11443631 035 $a(PQKBTitleCode)TC0000808068 035 $a(PQKBWorkID)10775590 035 $a(PQKB)11513692 035 $a(DE-He213)978-1-4612-1534-9 035 $a(MiAaPQ)EBC3076160 035 $a(PPN)237996499 035 $a(EXLCZ)993400000000089589 100 $a20121227d1999 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aProblems and Solutions for Complex Analysis$b[electronic resource] /$fby Rami Shakarchi 205 $a1st ed. 1999. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1999. 215 $a1 online resource (XI, 246 p. 17 illus.) 300 $a"With 46 illustrations." 311 $a0-387-98831-9 327 $aI Complex Numbers and Functions -- I.1 Definition -- I.2 Polar Form -- I.3 Complex Valued Functions -- I.4 Limits and Compact Sets -- I.6 The Cauchy-Riemann Equations -- II Power Series -- II.1 Formal Power Series -- II.2 Convergent Power Series -- II.3 Relations Between Formal and Convergent Series -- II.4 Analytic Functions -- II.5 Differentiation of Power Series -- II.6 The Inverse and Open Mapping Theorems -- III Cauchy?s Theorem, First Part -- III.1 Holomorphic Functions on Connected Sets -- III.2 Integrals over Paths -- III.5 The Homotopy Form of Cauchy?s Theorem -- III.6 Existence of Global Primitives Definition of the Logarithm -- III.7 The Local Cauchy Formula -- IV Winding Numbers and Cauchy?s Theorem -- IV.2 The Global Cauchy Theorem -- V Applications of Cauchy?s Integral Formula -- V.1 Uniform Limits of Analytic Functions -- V.2 Laurent Series -- V.3 Isolated Singularities -- VI Calculus of Residues -- VI.1 The Residue Formula -- VI.2 Evaluation of Definite Integrals -- VII Conformal Mappings -- VII.2 Analytic Automorphisms of the Disc -- VII.3 The Upper Half Plane -- VII.4 Other Examples -- VII.5 Fractional Linear Transformations -- VIII Harmonic Functions -- VIII.1 Definition -- VIII.2 Examples -- VIII.3 Basic Properties of Harmonic Functions -- VIII.4 The Poisson Formula -- VIII.5 Construction of Harmonic Functions -- IX Schwarz Reflection -- IX.2 Reflection Across Analytic Arcs -- X The Riemann Mapping Theorema -- X.1 Statement of the Theorem -- X.2 Compact Sets in Function Spaces -- XI Analytic Continuation along Curves -- XI.1 Continuation Along a Curve -- XI.2 The Dilogarithm -- XII Applications of the Maximum Modulus Principle and Jensen?s Formula -- XII.1 Jensen?s Formula -- XII.2 The Picard-Borel Theorem -- XII.6 The Phragmen-Lindelof and Hadamard Theorems -- XIII Entire and Meromorphic Functions -- XIII.1 Infinite Products -- XIII.2 Weierstrass Products -- XIII.3 Functions of Finite Order -- XIII.4 Meromorphic Functions, Mittag-Leffler Theorem -- XV The Gamma and Zeta Functions -- XV.1 The Differentiation Lemma -- XV.2 The Gamma Function -- XV.3 The Lerch Formula -- XV.4 Zeta Functions -- XVI The Prime Number Theorem -- XVI.1 Basic Analytic Properties of the Zeta Function -- XVI.2 The Main Lemma and its Application. 330 $aThis book contains all the exercises and solutions of Serge Lang's Complex Analy­ sis. Chapters I through VITI of Lang's book contain the material of an introductory course at the undergraduate level and the reader will find exercises in all of the fol­ lowing topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings and har­ monic functions. Chapters IX through XVI, which are suitable for a more advanced course at the graduate level, offer exercises in the following subjects: Schwarz re­ flection, analytic continuation, Jensen's formula, the Phragmen-LindelOf theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and the Zeta function. This solutions manual offers a large number of worked out exercises of varying difficulty. I thank Serge Lang for teaching me complex analysis with so much enthusiasm and passion, and for giving me the opportunity to work on this answer book. Without his patience and help, this project would be far from complete. I thank my brother Karim for always being an infinite source of inspiration and wisdom. Finally, I want to thank Mark McKee for his help on some problems and Jennifer Baltzell for the many years of support, friendship and complicity. Rami Shakarchi Princeton, New Jersey 1999 Contents Preface vii I Complex Numbers and Functions 1 1. 1 Definition . . . . . . . . . . 1 1. 2 Polar Form . . . . . . . . . 3 1. 3 Complex Valued Functions . 8 1. 4 Limits and Compact Sets . . 9 1. 6 The Cauchy-Riemann Equations . 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aAnalysis. 676 $a515/.9 700 $aShakarchi$b Rami$4aut$4http://id.loc.gov/vocabulary/relators/aut$061671 906 $aBOOK 912 $a9910480773503321 996 $aProblems and Solutions for Complex Analysis$92055599 997 $aUNINA LEADER 02021nas 2200553-a 450 001 996197773503316 005 20240413030128.0 011 $a1929-4603 035 $a(CKB)991042737753986 035 $a(CONSER)cn-90032273- 035 $a(DE-599)ZDB2539084-3 035 $a(EXLCZ)99991042737753986 100 $a19901105b19902005 --- b 101 0 $afre 200 00$aRevue francophone de la déficience intellectuelle 210 $aMontréal $c[s.n.$d1990-2005] 215 $a1 online resource 300 $aTitre pris sur la couv. 311 08$aPrint version: Revue francophone de la déficience intellectuelle. 0847-5733 (DLC)cn 90032273 (OCoLC)1081341504 531 0 $aRev. francoph. défic. intellect. 606 $aPeople with mental disabilities$vPeriodicals 606 $aHandicapés mentaux$vPériodiques 606 $aIntellectual disability$xResearch$vPeriodicals 606 $aDéficience intellectuelle$xRecherche$vPériodiques 606 $aIntellectual disability$xResearch$2fast$3(OCoLC)fst01016646 606 $aPeople with mental disabilities$2fast$3(OCoLC)fst01057383 606 $ahandicap mental$vpériodique$2rero 606 $ahandicapé mental$vpériodique$2rero 606 $ahandicap mental$2rerovoc 606 $ahandicapé mental$2rerovoc 608 $aPeriodicals.$2fast 608 $aPériodique.$2rerovoc 615 0$aPeople with mental disabilities 615 6$aHandicapés mentaux 615 0$aIntellectual disability$xResearch 615 6$aDéficience intellectuelle$xRecherche 615 7$aIntellectual disability$xResearch. 615 7$aPeople with mental disabilities. 615 7$ahandicap mental 615 7$ahandicapé mental 615 7$ahandicap mental. 615 7$ahandicapé mental. 676 $a616.8/588/005 686 $acci1icc$2lacc 906 $aJOURNAL 912 $a996197773503316 920 $aexl_impl conversion 996 $aRevue francophone de la déficience intellectuelle$91928411 997 $aUNISA