Hidden Harmony—Geometric Fantasies
The Rise of Complex Function Theory
Seiten
2016
|
Softcover reprint of the original 1st ed. 2013
Springer-Verlag New York Inc.
978-1-4939-4611-2 (ISBN)
Springer-Verlag New York Inc.
978-1-4939-4611-2 (ISBN)
This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl.
Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions.
The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.
Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions.
The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.
List of Figures.- Introduction.- 1. Elliptic Functions.- 2. From real to complex.- 3. Cauch.- 4. Elliptic integrals.- 5. Riemann.- 6. Weierstrass.- 7. Differential equations.- 8. Advanced topics.- 9. Several variables.- 10. Textbooks.
| Erscheinungsdatum | 04.10.2016 |
|---|---|
| Reihe/Serie | Sources and Studies in the History of Mathematics and Physical Sciences |
| Zusatzinfo | 2 Illustrations, color; 36 Illustrations, black and white; XVII, 848 p. 38 illus., 2 illus. in color. |
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik | |
| Schlagworte | Complex Function Theory • differential equations in the complex domain • elliptic function theory • Geometric Function Theory |
| ISBN-10 | 1-4939-4611-0 / 1493946110 |
| ISBN-13 | 978-1-4939-4611-2 / 9781493946112 |
| Zustand | Neuware |
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