Download E-books Differentialgeometrie. Kurven - Flächen - Mannigfaltigkeiten. PDF

By Wolfgang Kühnel

Dieses Buch ist eine Einführung in die Differentialgeometrie. Zunächst geht es um die klassischen Aspekte wie die Geometrie von Kurven und Flächen, bevor dann höherdimensionale Flächen sowie abstrakte Mannigfaltigkeiten betrachtet werden. Die Nahtstelle ist dabei das zentrale Kapitel "Die innere Geometrie von Flächen". Dieses führt den Leser bis hin zu dem berühmten Satz von Gauß-Bonnet, der ein entscheidendes Bindeglied zwischen lokaler und globaler Geometrie darstellt. Die zweite Hälfte des Buches ist der Riemannschen Geometrie gewidmet. Den Abschluss bildet ein Kapitel über "Einstein-Räume", die eine große Bedeutung sowohl in der "Reinen Mathematik" als auch in der Allgemeinen Relativitätstheorie von A. Einstein haben. Es wird großer Wert auf Anschaulichkeit gelegt, used to be durch zahlreiche Abbildungen unterstützt wird. Im Laufe der Neuauflagen wurde der textual content erweitert, neue Aufgaben wurden hinzugefügt und am Ende des Buches wurden zusätzliche Hinweise zur Lösung der Übungsaufgaben ergänzt. Der textual content wurde für die fünfte Auflage gründlich durchgesehen und an einigen Stellen verbessert.

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Download E-books Convex Sets and Their Applications (Dover Books on Mathematics) PDF

By Steven R. Lay

Suitable for complex undergraduates and graduate scholars, this article introduces the wide scope of convexity. It leads scholars to open questions and unsolved difficulties, and it highlights different purposes. writer Steven R. Lay, Professor of arithmetic at Lee collage in Tennessee, reinforces his teachings with various examples, plus routines with tricks and answers.
The first 3 chapters shape the basis for all that follows, beginning with a evaluate of the basics of linear algebra and topology. additionally they survey the advance and functions of relationships among hyperplanes and convex units. next chapters are fairly self-contained, every one targeting a specific point or software of convex units. themes comprise characterizations of convex units, polytopes, duality, optimization, and convex services. tricks, suggestions, and references for the workouts look in the back of the book.

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Download E-books Normal Forms and Bifurcation of Planar Vector Fields PDF

By Shui-Nee Chow

This ebook is principally desirous about the bifurcation conception of ODEs. Chapters 1 and a pair of of the e-book introduce systematic equipment of simplifying equations: heart manifold conception and general shape thought, in which one may possibly lessen the size of equations and alter varieties of equations to be so simple as attainable. Chapters 3-5 of the ebook research in substantial aspect the bifurcation of these one or dimensional equations with one, or a number of parameters.

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Download E-books Differential Geometry and its Applications: Proceedings of the 10th International Conference Dga 2007 Olomouc, Czech Republic 27-31 August 2007 by Demeter Krupka (2008-07-14) PDF

By Demeter Krupka;Olga Krupkova;Jan Slovak

This quantity includes invited lectures and chosen learn papers within the fields of classical and sleek differential geometry, international research, and geometric tools in physics, provided on the tenth foreign convention on Differential Geometry and its functions (DGA2007), held in Olomouc, Czech Republic. The e-book covers contemporary advancements and the newest leads to the subsequent fields: Riemannian geometry, connections, parabolic geometries, jets, differential invariants, the calculus of diversifications on manifolds, differential equations, Finsler buildings, and geometric equipment in physics. it's also a party of the three hundredth anniversary of the beginning of 1 of the best mathematicians, Leonhard Euler, and contains the Euler lecture "Leonhardt Euler - three hundred years on". The impressive members comprise: A Asada, Manuel de Leon, Jurgen Eichhorn, J-H Eschenburg, and Ivan Kolar.

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