Cantitate/Preț
Produs

Complex Analysis, Riemann Surfaces and Integrable Systems: Moscow Lectures, cartea 3

Autor Sergey M. Natanzon Traducere de Natalia Tsilevich
en Limba Engleză Paperback – 30 ian 2021
This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided.
We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications.
After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc.
The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.

Citește tot Restrânge

Toate formatele și edițiile

Toate formatele și edițiile Preț Express
Paperback (1) 37244 lei  6-8 săpt.
  Springer International Publishing – 30 ian 2021 37244 lei  6-8 săpt.
Hardback (1) 47717 lei  6-8 săpt.
  Springer International Publishing – 30 ian 2020 47717 lei  6-8 săpt.

Din seria Moscow Lectures

Preț: 37244 lei

Nou

Puncte Express: 559

Preț estimativ în valută:
7128 7410$ 5905£

Carte tipărită la comandă

Livrare economică 05-19 februarie 25

Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9783030346423
ISBN-10: 3030346420
Pagini: 139
Ilustrații: XIII, 139 p. 22 illus.
Dimensiuni: 155 x 235 x 13 mm
Greutate: 0.23 kg
Ediția:1st ed. 2019
Editura: Springer International Publishing
Colecția Springer
Seria Moscow Lectures

Locul publicării:Cham, Switzerland

Cuprins

Holomorphic functions.- Meromorphic functions.- Riemann's theorem.- Harmonic functions.- Riemann surfaces and their modules.- Compact Riemann surfaces and algebraic curves.- Riemann-Roch theorem and theta functions.- Integrable Systems.- The formula for the conformal mapping of an arbitrary domain into the unit disk.

Notă biografică

Sergey M. Natanzon is a professor of mathematics at the NRU Higher School of Economics since 2008, and a professor of mathematics at the Independent University of Moscow since 1991.

Textul de pe ultima copertă

This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided.
We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications.
After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc.
The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.


Caracteristici

Using basic tools from the first year of university studies, the book leads a reader to the impressive achievements of mathematics of the 21st century Studying the book, the reader will get acquainted with analytical and harmonic functions, as well as with the main results of the theory of Riemann surfaces. The reader will also get acquainted with the modern use of these results for solving classical problems of practical importance. These applications are based on the theory of integrable systems, which is also discussed in the book Practical all the statements are given in the book with full proofs