| 書目名稱 | From Real to Complex Analysis |
| 編輯 | R. H. Dyer,D. E. Edmunds |
| 視頻video | http://file.papertrans.cn/349/348900/348900.mp4 |
| 概述 | Provides a self-contained course in real and complex analysis that links analysis and topology.Approaches complex analysis through real analysis, with an overarching theme being the search for a primi |
| 叢書名稱 | Springer Undergraduate Mathematics Series |
| 圖書封面 |  |
| 描述 | .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 |
| 出版日期 | Textbook 2014 |
| 關鍵詞 | Elements of Complex Analysis; Jordan Curve Theorem; Metric Spaces; Riemann Integral on the Line; Riemann |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-06209-9 |
| isbn_softcover | 978-3-319-06208-2 |
| isbn_ebook | 978-3-319-06209-9Series ISSN 1615-2085 Series E-ISSN 2197-4144 |
| issn_series | 1615-2085 |
| copyright | Springer Nature Switzerland AG 2014 |
|Archiver|手機版|小黑屋|
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