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In Lectures on the Theory of Elliptic Functions, Vol. 1, Hancock presents a rigorous look at elliptic functions and their algebraic structure. The text surveys how one-valued functions with algebraic addition-theorems fit into rational, simply periodic, and doubly periodic realms, building from foundational ideas to far-reaching consequences.
The book emphasizes key theorems and the logical path from general principles to concrete results, including Liouville’s theorem and Briot and Bouquet’s perspectives. It clarifies how elliptic functions connect to Riemann surfaces and how inversion problems are resolved within a unified framework.
- Follow the development of algebraic addition-theorems for elliptic and related functions.
- See how rational functions of multiple variables describe one-valued functions on complex surfaces.
- Learn how elliptic integrals arise from general expressions and their normal forms.
- Gain perspective on the classification of functions by their periodicity and algebraic properties.
Ideal for readers who want a thorough, historical, and theory-driven view of elliptic functions and their applications in complex analysis.
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Paperback. Zustand: New. Print on Demand. This book delves into the intricate world of elliptic functions, exploring their historical development, mathematical foundations, and diverse applications. The author guides readers through the contributions of renowned mathematicians like Abel, Jacobi, and Weierstrass, illuminating the evolution of elliptic function theory from its origins to its more advanced forms. The book skillfully contrasts different approaches, such as the classical methods of Legendre and Jacobi with the modern insights of Weierstrass and Riemann, providing a comprehensive understanding of the subject. It delves into the realm of complex analysis, examining concepts like Riemann surfaces and the nature of periodicity, showcasing the profound connections between elliptic functions and other branches of mathematics, including algebra, geometry, and number theory. Through a blend of theoretical rigor and practical applications, this book offers valuable insights into the world of elliptic functions. It serves as a testament to the enduring power and elegance of mathematical thought, revealing how these functions have shaped our understanding of diverse scientific fields and continue to inspire new discoveries. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781440079597_0
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