Mathematics of the 19th Century : Geometry, Analytic Function Theory / edited by A. N. Kolmogorov, A. P. Yushkevich
| データ種別 | 電子ブック |
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| 出版者 | Basel : Birkhäuser Basel |
| 出版年 | 1996 |
| 本文言語 | 英語 |
| 大きさ | X, 291 p : online resource |
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| 内容注記 | 1. Geometry 1. Analytic and Differential Geometry 2. Projective Geometry 3. Algebraic Geometry and Geometric Algebra 4. Non-Euclidean Geometry 5. Multi-Dimensional Geometry 6. Topology 7. Geometric Transformations Conclusion 2. Analytic Function Results Achieved in Analytic Function Theory in the Eighteenth Century Development of the Concept of a Complex Number Complex Integration The Cauchy Integral Theorem. Residues Elliptic Functions in the Work of Gauss Hypergeometric Functions The First Approach to Modular Functions Power Series. The Method of Majorants Elliptic Functions in the Work of Abel C.G.J. Jacobi. Fundamenta nova functionum ellipticarum The Jacobi Theta Functions Elliptic Functions in the Work of Eisenstein and Liouville. The First Textbooks Abelian Integrals. Abel’s Theorem Quadruply Periodic Functions Summary of the Development of Analytic Function Theory over the First Half of the Nineteenth Century V. Puiseux. Algebraic Functions Bernhard Riemann Riemann’s Doctoral Dissertation. The Dirichlet Principle Conformal Mappings Karl Weierstrass Analytic Function Theory in Russia. Yu.V. Sokhotski? and the Sokhotski?-Casorati-Weierstrass Theorem Entire and Meromorphic Functions. Picard’s Theorem Abelian Functions Abelian Functions (Continuation) Automorphic Functions. Uniformization Sequences and Series of Analytic Functions Conclusion Literature (F. A. Medvedev) General Works Collected Works and Other Original Sources Auxiliary Literature to Chapter 1 Auxiliary Literature to Chapter 2 Index of Names (A. F. Lapko) |
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| 一般注記 | The general principles by which the editors and authors of the present edition have been guided were explained in the preface to the first volume of Mathemat ics of the 19th Century, which contains chapters on the history of mathematical logic, algebra, number theory, and probability theory (Nauka, Moscow 1978; En glish translation by Birkhiiuser Verlag, Basel-Boston-Berlin 1992). Circumstances beyond the control of the editors necessitated certain changes in the sequence of historical exposition of individual disciplines. The second volume contains two chapters: history of geometry and history of analytic function theory (including elliptic and Abelian functions); the size of the two chapters naturally entailed di viding them into sections. The history of differential and integral calculus, as well as computational mathematics, which we had planned to include in the second volume, will form part of the third volume. We remind our readers that the appendix of each volume contains a list of the most important literature and an index of names. The names of journals are given in abbreviated form and the volume and year of publication are indicated; if the actual year of publication differs from the nominal year, the latter is given in parentheses. The book History of Mathematics from Ancient Times to the Early Nineteenth Century [in Russian], which was published in the years 1970-1972, is cited in abbreviated form as HM (with volume and page number indicated). The first volume of the present series is cited as Bk. 1 (with page numbers) |
| 著者標目 | Kolmogorov, A. N. editor Yushkevich, A. P. editor SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical analysis LCSH:Analysis (Mathematics) LCSH:Geometry LCSH:History FREE:Mathematics FREE:History of Mathematical Sciences FREE:Geometry FREE:Analysis |
| 分 類 | DC23:510.9 |
| 巻冊次 | ISBN:9783034891738 
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| ISBN | 9783034891738 |
| URL | http://dx.doi.org/10.1007/978-3-0348-9173-8 |
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