Elliptic Integrals and Elliptic Functions
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Beschreibung
This book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses. These examples form prototypes of major ideas in modern mathematics and were a driving force of the subject in the eighteenth and nineteenth centuries. In addition to giving an account of the main topics of the theory, the book also describes many applications, both in mathematics and in physics. For the reader’s convenience, all necessary preliminaries on basic notions such as Riemann surfaces are explained to a level sufficient to read the book.
For each notion a clear motivation is given for its study, answering the question ‘Why do we consider such objects?’, and the theory is developed in a natural way that mirrors its historical development (e.g., ‘If there is such and such an object, then you would surely expect this one’). This feature sets this text apart from other books on the same theme, which are usually presented in a different order. Throughout, the concepts are augmented and clarified by numerous illustrations.
Suitable for undergraduate and graduate students of mathematics, the book will also be of interest to researchers who are not familiar with elliptic functions and integrals, as well as math enthusiasts.
This book gives a comprehensive introduction to those parts of the theory of elliptic integrals and elliptic functions which provide illuminating examples in complex analysis, but which are not often covered in regular university courses. These examples form prototypes of major ideas in modern mathematics and were a driving force of the subject in the eighteenth and nineteenth centuries. In addition to giving an account of the main topics of the theory, the book also describes many applications, both in mathematics and in physics. For the reader’s convenience, all necessary preliminaries on basic notions such as Riemann surfaces are explained to a level sufficient to read the book.
For each notion a clear motivation is given for its study, answering the question ‘Why do we consider such objects?’, and the theory is developed in a natural way that mirrors its historical development (e.g., ‘If there is such and such an object, then you would surely expect this one’). This feature sets this text apart from other books on the same theme, which are usually presented in a different order. Throughout, the concepts are augmented and clarified by numerous illustrations.
Suitable for undergraduate and graduate students of mathematics, the book will also be of interest to researchers who are not familiar with elliptic functions and integrals, as well as math enthusiasts.
Many applications to physics and to mathematics are introduced Clear motivation to each item (‘Why do we consider such objects?’) is given The theory is developed in a natural way of thinking
Autor*in
Takashi Takebe
Themen in »Elliptic Integrals and Elliptic Functions«
elliptic functions elliptic integrals complex analysis application to physics Riemann surfaces elliptic curves Abel-Jacobi theorem addition theorems theta functions
Stimmen zu »Elliptic Integrals and Elliptic Functions«
“This book is intended to present various aspects of the theory of elliptic integrals and elliptic functions, and provides definitions, theorems, proofs, examples and applications. … The book is well written and organized in a clear way. It includes many figures and graphs helpful in explaining the material in each chapter of the book.” (Faitori Omer Salem, zbMATH 1542.33001, 2024)
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