Buch, Englisch, 350 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 5562 g
Buch, Englisch, 350 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 5562 g
Reihe: Springer Undergraduate Mathematics Series
ISBN: 978-3-319-23714-5
Verlag: Springer International Publishing
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.
Zielgruppe
Upper undergraduate
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.