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Globale Analysis

Author: Ilka Agricola
Publisher: Springer-Verlag
ISBN: 3322929035
Size: 13.88 MB
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Das Anliegen des Buches ist es, die klassische Vektoranalysis unter Verwendung der Differentialformen darzulegen. Anwendungen der allgemeinen Stokeschen Formel in Analysis, Geometrie und Topologie werden besprochen. In weiteren Teilen des Buches werden die Integrierbarkeit Pfaffscher Systeme, die Flächentheorie in Euklidischen Räumen sowie Elemente der Lie-Gruppen, Mechanik, Thermodynamik und Elektrodynamik unter Verwendung der Differentialformen behandelt.

Global Analysis

Author: Ilka Agricola
Publisher: American Mathematical Soc.
ISBN: 0821829513
Size: 48.95 MB
Format: PDF, Kindle
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This book introduces the reader to the world of differential forms and their uses in geometry, analysis, and mathematical physics. It begins with a few basic topics, partly as review, then moves on to vector analysis on manifolds and the study of curves and surfaces in $3$-space. Lie groups and homogeneous spaces are discussed, providing the appropriate framework for introducing symmetry in both mathematical and physical contexts. The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics. There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics.

Differential Forms And Connections

Author: R. W. R. Darling
Publisher: Cambridge University Press
ISBN: 9780521468008
Size: 59.47 MB
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This book introduces the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--and covers both classical surface theory, the modern theory of connections, and curvature. Also included is a chapter on applications to theoretical physics. The author uses the powerful and concise calculus of differential forms throughout. Through the use of numerous concrete examples, the author develops computational skills in the familiar Euclidean context before exposing the reader to the more abstract setting of manifolds. The only prerequisites are multivariate calculus and linear algebra; no knowledge of topology is assumed. Nearly 200 exercises make the book ideal for both classroom use and self-study for advanced undergraduate and beginning graduate students in mathematics, physics, and engineering.

Geometrical Methods Of Mathematical Physics

Author: Bernard F. Schutz
Publisher: Cambridge University Press
ISBN: 9780521298872
Size: 66.77 MB
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For physicists and applied mathematicians working in the fields of relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This book provides an introduction to the concepts and techniques of modern differential theory, particularly Lie groups, Lie forms and differential forms.

Differential Geometric Methods In Mathematical Physics

Author: S. Sternberg
Publisher: Springer Science & Business Media
ISBN: 9781402003417
Size: 22.23 MB
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The following pages represent the Proceedings of the XI Annual Conference on Differential Geometric Methods in Mathematical Physics which was held in Jerusalem from August 5 through 11, 1982 under the auspices of the Tel Aviv University and the Israel Academy of Sciences and Humanities. In addition to the above mentioned institutions, partial financial support was received form the Bank Leumi Lelsrael Fund for International Conferences, the American Friends of the Tel Aviv Institute of Mathematical Sciences and the Mathematics and Physics Branch of the United States Army Research, Development and Standardization Group (UK). We are grateful to all of these organizations for their financial support. GAUGE THEORY AND NUCLEAR STRUCTURE K. Bleuler Institut fur Theoretische Kernphysik der Universitat Bonn NuBallee 14-16, D-5300 Bonn, West-Germany I. INTRODUCTION The recent, most impressive verification of the Salam­ -Weinberg theory of electro-weak interactions through the experimental discovery of the so-called inter­ mediate bosons represents, at the same time, a success of the general gauge theoretical viewpoints in modern particle physics (quantum chromodynamics, 0CD). This theory leads to a deeper and by far more natural inter­ pretation of particle interaction and induces, as we shall see, also a profound change in our understanding of nuclear structure.

Differential Geometry Gauge Theories And Gravity

Author: M. Göckeler
Publisher: Cambridge University Press
ISBN: 9780521378215
Size: 71.36 MB
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Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

Partial Differential Equations And Mathematical Physics

Author: Kunihiko Kajitani
Publisher: Springer Science & Business Media
ISBN: 1461200113
Size: 40.70 MB
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The 17 invited research articles in this volume, all written by leading experts in their respective fields, are dedicated to the great French mathematician Jean Leray. A wide range of topics with significant new results---detailed proofs---are presented in the areas of partial differential equations, complex analysis, and mathematical physics. Key subjects are: * Treated from the mathematical physics viewpoint: nonlinear stability of an expanding universe, the compressible Euler equation, spin groups and the Leray--Maslov index, * Linked to the Cauchy problem: an intermediate case between effective hyperbolicity and the Levi condition, global Cauchy--Kowalewski theorem in some Gevrey classes, the analytic continuation of the solution, necessary conditions for hyperbolic systems, well posedness in the Gevrey class, uniformly diagonalizable systems and reduced dimension, and monodromy of ramified Cauchy problem. Additional articles examine results on: * Local solvability for a system of partial differential operators, * The hypoellipticity of second order operators, * Differential forms and Hodge theory on analytic spaces, * Subelliptic operators and sub- Riemannian geometry. Contributors: V. Ancona, R. Beals, A. Bove, R. Camales, Y. Choquet- Bruhat, F. Colombini, M. De Gosson, S. De Gosson, M. Di Flaviano, B. Gaveau, D. Gourdin, P. Greiner, Y. Hamada, K. Kajitani, M. Mechab, K. Mizohata, V. Moncrief, N. Nakazawa, T. Nishitani, Y. Ohya, T. Okaji, S. Ouchi, S. Spagnolo, J. Vaillant, C. Wagschal, S. Wakabayashi The book is suitable as a reference text for graduate students and active researchers.