Elliptic Integrals and Elliptic Functions

Takashi Takebe

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English

Springer International Publishing AG
11 July 2023

Complex analysis, complex variables; Functional analysis & transforms; Mathematical physics

Series: Moscow Lectures

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.

By: Takashi Takebe
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2023 ed.
Volume: 9
Dimensions: Height: 235mm, Width: 155mm,
Weight: 676g
ISBN: 9783031302640
ISBN 10: 3031302648
Series: Moscow Lectures
Pages: 328
Publication Date: 11 July 2023
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Takashi TAKEBE is a professor at the Faculty of Mathematics, National Research University Higher School of Economics, Moscow. He studies integrable systems in mathematical physics, especially integrable nonlinear differential equations, their connection with complex analysis and solvable lattice models in statistical mechanics related to elliptic R-matrices.

Reviews for 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)