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Review: Modern Geometry Methods and Applications: Part I: The Geometry of Surfaces, Transformation Groups, and FieldsUser Review - Joecolelife - Goodreads
1. He presents pretty much every idea in multiple ways and from multiple viewpoints, illustrating the ubiquity and flexibility of the ideas. 2. He gives concrete examples of the concepts so you can ... Read full review
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3-dimensional analytic arbitrary Cartesian co-ordinate change co-ordinate system co-ordinates x1 co-ordinatized commutator completes the proof complex components connexion consider const constant corresponding covector curve defined definition denote derivative electromagnetic field element Euclidean 3-space Euclidean co-ordinates Euclidean metric Euler-Lagrange equations example expression follows formula function Gaussian curvature geodesic geometry given GL(n gradient Hamiltonian Hence identity integral invariant isometries isomorphic Jacobian Lagrangian lattice Lemma Lie algebra linear transformation Lorentz Lorentz transformation matrix metric gu Minkowski Minkowski space momentum neighbourhood non-zero notation Note obtain operation orthogonal parameter particle particular phase space pseudo-Euclidean quadratic form region relative respect Riemannian Riemannian metric right-hand side rotation satisfying scalar product skew-symmetric skew-symmetric tensor smooth sphere spinor Stokes formula subgroup Suppose symmetric tangent space tangent vector tensor of type Theorem theory translations underlying space vector field velocity whence zero
Page 462 - Electrodynamics of Continuous Media, Course of Theoretical Physics, Vol. 8, Pergamon Press, Oxford, UK, 1982.
Page vi - Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in...
Page vi - The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University.
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