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The real and the complex[electronic resource] :a history of analysis in the 19th century /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.9
書名/作者:	The real and the complex : a history of analysis in the 19th century // by Jeremy Gray.
作者:	Gray, Jeremy.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xvi, 350 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Mathematical analysis - History - 19th century.
標題:	Mathematics.
標題:	Functions of a Complex Variable.
標題:	Real Functions.
標題:	History of Mathematical Sciences.
ISBN:	9783319237152
ISBN:	9783319237145
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-23715-2

The real and the complex[electronic resource] :a history of analysis in the 19th century /
Gray, Jeremy.

The real and the complexa history of analysis in the 19th century /[electronic resource] :by Jeremy Gray. - Cham :Springer International Publishing :2015. - xvi, 350 p. :ill., digital ;24 cm. - Springer undergraduate mathematics series,1615-2085. - Springer undergraduate mathematics series..

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.

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.

ISBN: 9783319237152

Standard No.: 10.1007/978-3-319-23715-2doiSubjects--Topical Terms:

635735
Mathematical analysis
--History--19th century.

LC Class. No.: QA300

Dewey Class. No.: 515.9

The real and the complex[electronic resource] :a history of analysis in the 19th century /
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