The Real and the Complex: A History of Ana...

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Jeremy Gray is a leading historian of modern mathematics. He has been awarded the Leon Whiteman Prize of the American Mathematical Society and the Neugebauer Prize of the European Mathematical Society for his work, and is a Fellow of the American Mathematical Society.

Zusammenfassung

Introduces key ideas in real and complex analysis in the manner they were discovered

Motivates and explains many related developments in neighbouring fields, including number theory, elliptic function theory, and potential theory

Displays many examples illustrating the merits of rigorous analysis

Includes supplementary material: [...]

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2015
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Undergraduate Mathematics Series
Inhalt:	xvi 350 S. 71 s/w Illustr. 350 p. 71 illus.
ISBN-13:	9783319237145
ISBN-10:	3319237144
Sprache:	Englisch
Herstellernummer:	978-3-319-23714-5
Einband:	Kartoniert / Broschiert
Autor:	Gray, Jeremy
Auflage:	1st edition 2015
Hersteller:	Springer Springer International Publishing AG Springer Undergraduate Mathematics Series
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 20 mm
Von/Mit:	Jeremy Gray
Erscheinungsdatum:	05.11.2015
Gewicht:	0,557 kg