LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	515.9
Title	The Real and the Complex: A History of Analysis in the 19th Century ([EBook]) / by Jeremy Gray.
Author	Gray, Jeremy J. , 1947-
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2015.
Publication	Cham : Springer International Publishing , 2015.
Physical Details	XVI, 350 pages, 71 illus. : online resource.
Series	Springer undergraduate mathematics series 1615-2085
ISBN	9783319237152
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-23715-2
Links to Related Works	Subject References: Functions of a Complex Variable . Functions of complex variables . Functions of real variables . History . History of Mathematical Sciences . Mathematics . Mathematics - History . Real Functions . Authors: Gray, Jeremy J. 1947- . Gray, Jeremy J., 1947- . Corporate Authors: SpringerLink (Online service) . Series: Springer undergraduate mathematics series . Classification: 515.9 .

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The Real and the Complex: A History of Analysis in the 19th Century

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