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

• Κύριος συγγραφέας: Gray, Jeremy (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Έκδοση: 1st ed. 2015.
• Σειρά: Springer Undergraduate Mathematics Series,
• Θέματα: Mathematics.; Functions of complex variables.; Functions of real variables.; History.; Functions of a Complex Variable.; Real Functions.; History of Mathematical Sciences.

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 un...

Πίνακας περιεχομένων:

• 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.