Moscow Lectures

Complex Analysis, Riemann Surfaces and Integrable Systems

Authors: Natanzon, Sergey M.

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  • 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
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eBook 21,39 €
46,00 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-34640-9
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Hardcover 29,11 €
57,19 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-34639-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
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Softcover 29,11 €
57,19 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-34642-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.


About the authors

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.

Table of contents (9 chapters)

Table of contents (9 chapters)
  • Holomorphic Functions

    Pages 1-17

    Natanzon, Sergey M.

  • Meromorphic Functions

    Pages 19-28

    Natanzon, Sergey M.

  • Riemann Mapping Theorem

    Pages 29-35

    Natanzon, Sergey M.

  • Harmonic Functions

    Pages 37-44

    Natanzon, Sergey M.

  • Riemann Surfaces and Their Modules

    Pages 45-68

    Natanzon, Sergey M.

Buy this book

eBook 21,39 €
46,00 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-34640-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 29,11 €
57,19 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-34639-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 29,11 €
57,19 € (listprice)
price for Spain (gross)
valid through June 30, 2021
  • ISBN 978-3-030-34642-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions & severe weather in the US may cause delays
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Complex Analysis, Riemann Surfaces and Integrable Systems
Authors
Translated by
Tsilevich, N.
Series Title
Moscow Lectures
Series Volume
3
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-34640-9
DOI
10.1007/978-3-030-34640-9
Hardcover ISBN
978-3-030-34639-3
Softcover ISBN
978-3-030-34642-3
Series ISSN
2522-0314
Edition Number
1
Number of Pages
XIII, 139
Number of Illustrations
22 b/w illustrations
Topics