By Umberto Bottazzini,Jeremy Gray
This publication is a historical past of advanced functionality idea from its origins to 1914, while the fundamental positive factors of the trendy idea have been in position. it's the first historical past of arithmetic dedicated to complicated functionality thought, and it attracts on a variety of released and unpublished resources. as well as an in depth and distinctive assurance of the 3 founders of the topic – Cauchy, Riemann, and Weierstrass – it appears on the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl.
Particular chapters learn the increase and value of elliptic functionality concept, differential equations within the advanced area, geometric functionality concept, and the early years of complicated functionality idea in different variables. specified emphasis has been dedicated to the construction of a textbook culture in complicated research by means of contemplating a few seventy textbooks in 9 diverse languages. The ebook isn't a trifling series of disembodied effects and theories, yet deals a finished photo of the wide cultural and social context within which the most actors lived and labored by means of being attentive to the increase of mathematical faculties and of contrasting nationwide traditions.
The booklet is unmatched for its breadth and intensity, either within the middle idea and its implications for different fields of arithmetic. It records the motivations for the early rules and their sluggish refinement right into a rigorous theory.
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Additional resources for Hidden Harmony—Geometric Fantasies: The Rise of Complex Function Theory (Sources and Studies in the History of Mathematics and Physical Sciences)
Hidden Harmony—Geometric Fantasies: The Rise of Complex Function Theory (Sources and Studies in the History of Mathematics and Physical Sciences) by Umberto Bottazzini,Jeremy Gray