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From real to complex analysis

The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology. Beginning with the theory of the Riemann integral (and its improper...

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Detalles Bibliográficos
Autores principales: Dyer, R H, Edmunds, D E
Lenguaje:eng
Publicado: Springer 2014
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-319-06209-9
http://cds.cern.ch/record/1707522
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author Dyer, R H
Edmunds, D E
author_facet Dyer, R H
Edmunds, D E
author_sort Dyer, R H
collection CERN
description The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology. Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectedness and various forms of homotopy. The final chapter develops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using the approach due to Dixon. Special features are the inclusion of proofs of Montel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included in each of the chapters, detailed solutions of the majority of which are given at the end. From Real to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding in analysis; in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be made.
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spelling cern-17075222021-04-21T20:58:35Zdoi:10.1007/978-3-319-06209-9http://cds.cern.ch/record/1707522engDyer, R HEdmunds, D EFrom real to complex analysisMathematical Physics and MathematicsThe purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology. Beginning with the theory of the Riemann integral (and its improper extension) on the real line, the fundamentals of metric spaces are then developed, with special attention being paid to connectedness, simple connectedness and various forms of homotopy. The final chapter develops the theory of complex analysis, in which emphasis is placed on the argument, the winding number, and a general (homology) version of Cauchy's theorem which is proved using the approach due to Dixon. Special features are the inclusion of proofs of Montel's theorem, the Riemann mapping theorem and the Jordan curve theorem that arise naturally from the earlier development. Extensive exercises are included in each of the chapters, detailed solutions of the majority of which are given at the end. From Real to Complex Analysis is aimed at senior undergraduates and beginning graduate students in mathematics. It offers a sound grounding in analysis; in particular, it gives a solid base in complex analysis from which progress to more advanced topics may be made.Springeroai:cds.cern.ch:17075222014
spellingShingle Mathematical Physics and Mathematics
Dyer, R H
Edmunds, D E
From real to complex analysis
title From real to complex analysis
title_full From real to complex analysis
title_fullStr From real to complex analysis
title_full_unstemmed From real to complex analysis
title_short From real to complex analysis
title_sort from real to complex analysis
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-319-06209-9
http://cds.cern.ch/record/1707522
work_keys_str_mv AT dyerrh fromrealtocomplexanalysis
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