The Real and the Complex: A History of Analysis in the 19th Century / by Jeremy Gray
| データ種別 | 電子書籍 |
|---|---|
| 版 | 1st ed. 2015. |
| 出版者 | Cham : Springer International Publishing : Imprint: Springer |
| 出版年 | 2015 |
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| 書誌ID | OB01016868 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | Lagrange and foundations for the calculus -- Joseph Fourier -- Legendre -- Cauchy and continuity -- Cauchy: differentiation and integration -- Cauchy and complex functions to 1830 -- Abel -- Jacobi -- Gauss -- Cauchy and complex function theory, 1830-1857 -- Complex functions and elliptic integrals -- Revision -- Gauss, Green, and potential theory -- Dirichlet, potential theory, and Fourier series -- Riemann -- Riemann and complex function theory -- Riemann's later complex function theory -- Responses to Riemann's work -- Weierstrass -- Weierstrass's foundational results -- Revision { and assessment -- Uniform Convergence -- Integration and trigonometric series -- The fundamental theorem of the calculus -- The construction of the real numbers -- Implicit functions -- Towards Lebesgue's theory of integration -- Cantor, set theory, and foundations -- Topology -- Assessment. License restrictions may limit access Summary: This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis |
| 著者標目 | *Gray, Jeremy SpringerLink (Online service) |
| 統一書名標目 | Springer Undergraduate Mathematics Series, |
| 件 名 | LCSH:Mathematics LCSH:Functions of complex variables LCSH:Functions of real variables LCSH:History FREE:Mathematics FREE:Functions of a Complex Variable FREE:Real Functions FREE:History of Mathematical Sciences |
| 分 類 | LCC:QA331-355 DC23:515.9 |
| 巻冊次 | ISBN:9783319237152 RefWorks出力（各巻） print ; ISBN:9783319237145 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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