By Keith Burns,Marian Gidea
Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential kinds, and integration on manifolds give you the origin for lots of purposes in dynamical platforms and mechanics. The authors additionally speak about the Gauss-Bonnet theorem and its implications in non-Euclidean geometry versions.
The differential topology point of the ebook facilities on classical, transversality conception, Sard's theorem, intersection thought, and fixed-point theorems. the development of the de Rham cohomology builds additional arguments for the powerful connection among the differential constitution and the topological constitution. It additionally furnishes many of the instruments priceless for a whole knowing of the Morse idea. those discussions are by way of an creation to the idea of hyperbolic structures, with emphasis at the necessary function of the geodesic circulate.
The integration of geometric idea, topological conception, and urban purposes to dynamical platforms set this ebook aside. With fresh, transparent prose and powerful examples, the authors' intuitive method creates a remedy that's understandable to relative novices, but rigorous sufficient for people with extra history and event within the field.
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Differential Geometry and Topology: With a View to Dynamical Systems (Studies in Advanced Mathematics) by Keith Burns,Marian Gidea
by Robert
4.2
