Verfügbarkeit: Fundamentals and applications of complex analysis

Fundamentals and applications of complex analysis:

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1. Verfasser:	Cohen, Harold (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	New York [u.a.] Kluwer 2003
Schlagworte:	Funktionentheorie Konforme Abbildung
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XIV, 418 S. graph. Darst.
ISBN:	0306477483

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Datensatz im Suchindex

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adam_text	Titel: Fundamentals and applications of complex analysis Autor: Cohen, Harold Jahr: 2003 Contents 1 INTRODUCTION................................................................................1 1.1 A BRIEF HISTORY......................................................................1 2 COMPLEX NUMBERS.......................................................................5 2.1 CONJUGATION, MODULUS, ARGUMENT AND ARITHEMTIC...............................................................................5 2.2 CARTESIAN, TRIGONOMETRIC AND POLAR FORMS.........11 2.3 ROOTS OF UNITY.....................................................................19 2.4 COMPLEX NUMBERS AND AC CIRCUITS ............................23 PROBLEMS.......................................................................................33 3 COMPLEX VARIABLES...................................................................39 3.1 DERIVATIVES, CAUCHY-RIEMANN CONDITIONS AND ANALYTICITY...........................................................................39 3.2 INTEGRALS OF ANALYTIC FUNCTION.................................50 3.3 POLE SINGULARITIES.............................................................54 3.4 CAUCHY S RESIDUE THEOREM............................................59 PROBLEMS.......................................................................................74 4 SERIES, LIMITS AND RESIDUES....................................................79 4.1 TAYLOR SERIES FOR ANALYTIC FUNCTIONS...................79 4.2 LAURENT SERIES FOR A SINGULAR FUNCTION...............84 4.3 ARITHMETIC COMBINATIONS OF POWER SERIES............91 4.4 LIMITS AND L HOSPITAL S RULE.........................................97 4.5 RESIDUES ...............................................................................101 PROBLEMS.....................................................................................Ill Contents xiv 5 EVALUATION OF INTEGRALS............................................... 5 I INTEGRALS ALONG THE ENTIRE REAL AXIS............. 5.2 INTEGRALS OF FUNCTIONS OF SIN0 AND COS0...... 5.3 CAUCHY S PRINCIPAL VALUE INTEGRAL AND THE DIRAC 5 SYMBOL........................................................ 5.4 MISCELLANEOUS INTEGRALS................................. PROBLEMS.......................................................................... 6 MULTIVALUED FUNCTIONS, BRANCH POINTS AND CUTS.................................................................................... 6.1 NON-INTEGER POWER, LOGARITHM FUNCTIONS 6.2 RIEMANN SHEETS, BRANCH POINTS AND CUTS.. 6.3 BRANCH STRUCTURE................................................. 6.4 MULTIPLE BRANCH POINTS...................................... 6.5 EVALUATION OF INTEGRALS................................... PROBLEMS.......................................................................... 7 SINGULARITIES OF FUNCTIONS DEFINED BY INTEGRALS...215 7.1 THE INTEGRAND IS ANALYTIC...........................................215 7.2 THE INTEGRAND IS SINGULAR...........................................216 7.3 LIMITS OF THE INTEGRAL ARE VARIABLE.......................231 PROBLEMS.....................................................................................235 8 CONFORMAL MAPPING ...............................................................239 8.1 PROPERTIES OF A MAPPING................................................239 8.2 LINEAR AND BILINEAR TRANSFORMATIONS..................261 8.3 SCHWARZ-CHRISTOFFEL TRANSFORMATION.................272 8.4 APPLICATIONS.......................................................................301 PROBLEMS.....................................................................................336 9 DISPERSION RELATIONS.............................................................357 9.1 KRAMERS-KRONIG DISPERSION RELATIONS OVER THE ENTIRE REAL AXIS.................................................................358 9.2 KRAMERS-KRONIG DISPERSION RELATIONS OVER HALF THE REAL AXIS.......................................................................362 9.3 DISPERSION RELATIONS FOR A FUNCTION WITH BRANCH STRUCTURE............................................................................366 9.4 SUBTRACTED DISPERSION RELATIONS............................371 9.5 DISPERSION RELATIONS AND A REPRESENTATION OF THE DIRAC 5-SYMBOL..........................................................380 PROBLEMS.............................. 119 119 129 130 141 150 157 .158 162 167 178 191 209 Contents xv APPENDIX 1 DERIVATION OF GREEN S THEOREM......................389 APPENDIX 2 DERIVATION OF THE GEOMETRIC SERIES..............395 APPENDIX 3 EVALUATION OF AN INTEGRAL...............................397 APPENDIX 4 TRANSFORMATION OF LAPLACE S EQUATION.....401 APPENDIX 5 TRANSFORMATION OF BOUNDARY CONDITIONS.405 REFERENCES.......................................................................................411 INDEX...................................................................................................413
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author	Cohen, Harold
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dewey-ones	515 - Analysis
dewey-raw	515.9
dewey-search	515.9
dewey-sort	3515.9
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
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spelling	Cohen, Harold Verfasser aut Fundamentals and applications of complex analysis Harold Cohen New York [u.a.] Kluwer 2003 XIV, 418 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Konforme Abbildung (DE-588)4164968-0 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s Konforme Abbildung (DE-588)4164968-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019941702&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Cohen, Harold Fundamentals and applications of complex analysis Funktionentheorie (DE-588)4018935-1 gnd Konforme Abbildung (DE-588)4164968-0 gnd
subject_GND	(DE-588)4018935-1 (DE-588)4164968-0
title	Fundamentals and applications of complex analysis
title_auth	Fundamentals and applications of complex analysis
title_exact_search	Fundamentals and applications of complex analysis
title_full	Fundamentals and applications of complex analysis Harold Cohen
title_fullStr	Fundamentals and applications of complex analysis Harold Cohen
title_full_unstemmed	Fundamentals and applications of complex analysis Harold Cohen
title_short	Fundamentals and applications of complex analysis
title_sort	fundamentals and applications of complex analysis
topic	Funktionentheorie (DE-588)4018935-1 gnd Konforme Abbildung (DE-588)4164968-0 gnd
topic_facet	Funktionentheorie Konforme Abbildung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019941702&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT cohenharold fundamentalsandapplicationsofcomplexanalysis

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