Titlebook: Differential Geometry and Mathematical Physics; Part I. Manifolds, L Gerd Rudolph,Matthias Schmidt Book 2013 Springer Science+Business Medi

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Three-Dimensional Approximationhe theory of integration and the Stokes Theorem, as well as an introduction to de Rham cohomology. Next, we discuss elements of Riemannian geometry and Hodge duality. As an application, we show how classical Maxwell electrodynamics can be understood in a coordinate-free way using the language of dif

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Three-Dimensional Approximationlassical groups. Thereafter, we discuss left-invariant vector fields, define the Lie algebra of a Lie group and construct the exponential mapping, which provides a local diffeomorphism between the group and its algebra. This proves useful both for the study of the local structure of Lie groups and f

失望昨天

A New View of Scientific Rationalityfields of a special type, called Killing vector fields. We prove the Orbit Theorem, which states that the distribution spanned by the Killing vector fields is integrable and that its integral manifolds coincide with the connected components of the orbits of the action. This way, every orbit gets end

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Methodology, Heuristics, and Rationalitymplectic geometry provides the natural mathematical framework for the study of Hamiltonian systems. In this chapter, we present linear symplectic algebra. We start with a discussion of the elementary properties of symplectic vector spaces, the various types of their subspaces and linear symplectic r

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https://doi.org/10.1007/978-1-349-14936-0 are locally equivalent. Thus, in sharp contrast to the situation in Riemannian geometry, symplectic manifolds of the same dimension can at most differ globally. The second important observation is that a symplectic structure provides a duality between smooth functions and certain vector fields, cal

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On Non-Welfarist Social Ordering Functionsatical physics. On the one hand, it builds a bridge between classical mechanics and other branches of physics, in particular, optics. On the other hand, it yields a link between classical and quantum theory. We start with deriving the Hamilton-Jacobi equation and proving the classical Jacobi Theorem

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