The Real and the Complex: A History of Analysis in the 19th Century
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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.
Format:Paperback
Language:English
ISBN:3319237144
ISBN13:9783319237145
Release Date:November 2015
Publisher:Springer
Length:350 Pages
Weight:1.13 lbs.
Dimensions:0.8" x 6.1" x 9.2"
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