| 書目名稱 | Topology, Calculus and Approximation | | 編輯 | Vilmos Komornik | | 視頻video | http://file.papertrans.cn/927/926519/926519.mp4 | | 概述 | Includes the theory of nets to study arbitrary topological spaces.Illustrates the insufficiency of sequences with simple but rarely presented examples.Elaborates on the historical background of most n | | 叢書名稱 | Springer Undergraduate Mathematics Series | | 圖書封面 |  | | 描述 | Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erd?s, Fejér, Stieltjes, and Turán.?.The exposition style of .Topology, Calculus and Approximation. follows the Hungarian mathematical tradition of Paul Erd?s and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory‘s definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations..Students of both pure and applied mathematics, as well as physics and engineering should find this textbook useful. Only basic results of one-variable calculus and linear algebra are used, and simple ye | | 出版日期 | Textbook 2017 | | 關鍵詞 | metric space; normed space; topology; calculus; differential equations; implicit functions; interpolation; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4471-7316-8 | | isbn_softcover | 978-1-4471-7315-1 | | isbn_ebook | 978-1-4471-7316-8Series ISSN 1615-2085 Series E-ISSN 2197-4144 | | issn_series | 1615-2085 | | copyright | Springer-Verlag London Ltd. 2017 |
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