| 书目名称 | Essential Real Analysis | | 编辑 | Michael Field | | 视频video | | | 概述 | Contains more than 570 exercises of varying difficulty.Provides proofs of basic results on existence and regularity of solutions of ordinary differential equations.Includes a full treatment of the inv | | 丛书名称 | Springer Undergraduate Mathematics Series | | 图书封面 |  | | 描述 | .This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses..Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations andfractals.. .Essential Real Analysis .will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including | | 出版日期 | Textbook 2017 | | 关键词 | use of euler maclaurin formula; Euler-Maclaurin formula; metric space theory; metric space in real anal | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-67546-6 | | isbn_softcover | 978-3-319-67545-9 | | isbn_ebook | 978-3-319-67546-6Series ISSN 1615-2085 Series E-ISSN 2197-4144 | | issn_series | 1615-2085 | | copyright | Springer International Publishing AG 2017 |
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发表于 2025-3-21 16:21:27
