Elliptic Integrals and Elliptic Functions
Takashi Takebe
ΠΈΡΠ»Ρ 2023β―Π³. Β· Moscow Lectures ΠΠ½ΠΈΠ³Π°Β 9 Β· Springer Nature
ΠΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π°Ρ ΠΊΠ½ΠΈΠ³Π°
328
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ΠΠ± ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½ΠΎΠΉ ΠΊΠ½ΠΈΠ³Π΅
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 readerβs 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 βWhy do we consider such objects?β, and the theory is developed in a natural way that mirrors its historical development (e.g., βIf there is such and such an object, then you would surely expect this oneβ). 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.
ΠΠ± Π°Π²ΡΠΎΡΠ΅
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.
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