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Complex and Differential Geometry
This volume contains the Proceedings of the conference "Complex and Differential Geometry 2009", held at Leibniz Universität Hannover, September 14 - 18, 2009. It was the aim of this conference to bring specialists from differential geometry and (complex) algebraic geometry together and to discuss new developments in and the interaction between these fields. Correspondingly, the articles in this book cover a wide area of topics, ranging from topics in (classical) algebraic geometry through complex geometry, including (holomorphic) symplectic and poisson geometry, to differential geometry (with an emphasis on curvature flows) and topology.
Partial Differential Equations
This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research ...
Postmodern Analysis
What is the title of this book intended to signify, what connotations is the adjective "Postmodern" meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the approach to analysis presented here from what has been called "Modern Analysis" by its protagonists. "Modern Analysis" as represented in the works of the Bour baki group or in the textbooks by Jean Dieudonne is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degen erate into a collection of rather unconnected tricks to solve special problems, this definite...
Geometric Methods in Physics
The Białowieża workshops on Geometric Methods in Physics, taking place in the unique environment of the Białowieża natural forest in Poland, are among the important meetings in the field. Every year some 80 to 100 participants both from mathematics and physics join to discuss new developments and to interchange ideas. The current volume was produced on the occasion of the XXXI meeting in 2012. For the first time the workshop was followed by a School on Geometry and Physics, which consisted of advanced lectures for graduate students and young researchers. Selected speakers of the workshop were asked to contribute, and additional review articles were added. The selection shows that despite its now long tradition the workshop remains always at the cutting edge of ongoing research. The XXXI workshop had as a special topic the works of the late Boris Vasilievich Fedosov (1938–2011) who is best known for a simple and very natural construction of a deformation quantization for any symplectic manifold, and for his contributions to index theory.
Geometric Theory of Singular Phenomena in Partial Differential Equations
Featuring contributions from a group of outstanding mathematicians, this book covers the most recent advances in the geometric theory of singular phenomena of partial differential equations occurring in real and complex differential geometry. Gathering together papers from a workshop held in Cortona, Italy, this volume will be of great interest to all those whose research interests lie in real and complex differential geometry, partial differential equations, and gauge theory.
Analysis 1
Dieses Buch bietet eine kompakte und fundierte Einführung in die Analysis 1, wie sie an den meisten deutschen Universitäten gelehrt wird. Der Fokus liegt darauf, die wesentlichen Konzepte der Analysis klar und verständlich zu vermitteln, ohne den Leser mit unnötigem Ballast zu überfrachten. Durch die sorgfältige Auswahl der Inhalte bleibt der Blick auf das Wesentliche gerichtet, sodass die Grundlagen der Theorie optimal erfasst werden können. Ergänzt wird das Lehrbuch durch umfangreiches Übungsmaterial mit ausführlichen Lösungen, das den Lernprozess unterstützt und das Verständnis der Inhalte nachhaltig vertieft. Ideal für Studierende, die einen klaren, strukturierten Zugang zur Analysis suchen.
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