From real to complex analysis [Documento electrónico] / R. H. Dyer, D. E. Edmunds
Language: eng.Country: Germany.Publication: Cham : Springer International Publishing, 2014Description: X, 332 p. : il.ISBN: 978-3-319-06209-9.Series: Springer Undergraduate Mathematics SeriesSubject - Topical Name: 108Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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QA300.SPR FCT 81787 Introduction to mathematical analysis | QA300.SPR FCT 81863 Multi-band effective mass approximations, advanced mathematical models and numerical techniques | QA300.SPR FCT 81885 Locally convex spaces | QA300.SPR FCT 82012 From real to complex analysis | QA300.SPR FCT 82023 Topics in mathematical analysis and applications | QA300.SPR FCT 82030 Analysis and modeling of complex data in behavioral and social sciences | QA300.SPR FCT 82037 Advances in applied mathematics |
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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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