Overview
Die Theorie Riemannscher Flächen wird als ein Mikrokosmos der Reinen Mathematik dargestellt, in dem Methoden der Topologie und Geometrie, der komplexen und reellen Analysis sowie der Algebra zusammenwirken, um die reichhaltige Struktur dieser Flächen aufzuklären. Viele Beispiele und Bilder, die in der historischen Entwicklung eine Rolle spielten, ergänzen die Darstellung. Das Buch beruht auf Vorlesungen und Seminaren im Anschluß an eine Einführung in die komplexe Funktionentheorie. Wegen seiner Methodenvielfalt enthält es gleichzeitig Einführungen in die Topologie (Fundamentalgruppe, Überlagerungen, Flächen), in die algebraische Geometrie (Kurven und ihre Singularitäten) und in die Potentialtheorie (harmonische Funktionen). Die 2. Auflage wurde um eine genauere Betrachtung des Kleinschen 14-Ecks, ein Kapitel über die de Rhamsche Cohomologie und einen Paragraphen über die Lösung nicht-linearer Gleichungen der Mathematischen Physik mittels Riemannscher Thetafunktionen ergänzt.
Full Product Details
Author: Klaus Lamotke
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2., erg. u. verb. Aufl. 2009
Dimensions:
Width: 15.50cm
, Height: 1.80cm
, Length: 23.50cm
Weight: 0.534kg
ISBN: 9783642017100
ISBN 10: 364201710
Pages: 341
Publication Date: 26 June 2009
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: In Print
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Language: German
Reviews
From the reviews of the second edition: The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009) From the reviews of the second edition: The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. ... This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009) From the reviews of the second edition: The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009)
From the reviews of the second edition: The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009)
From the reviews of the second edition: “The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. … This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered.” (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009)
<p>From the reviews of the second edition: <p> The theory of Riemann surfaces is the mierocosin of pure mathematics, in which the methods of topology and geometry, complex and real analysis is well as of the algebra interactt to illuminate and to explain the structure of these surfaces. This second enlarged and revised edition of the book contains a new chapter on the de Rham cohomology of Riemann surfaces, in which Pfaff forins, surface forins, ring domains, disks Hodge decompositions period matrices, and normalized differential forms are considered. (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009)
