Applications of Lie groups to differential equations Peter J. Olver
Publisher: Springer-Verlag

Topics include: Lie groups & Lie algebras, differential geometry (vector fields, Riemannian metrics, covariant derivatives, geodesics, Killing vector fields), Lie groups and differential equations and the calculus of variations. Here differential geometry is developed. The book contains exercises and plenty of worked examples. Introduced his revolutionary ideas, some of these proposed independently by Yuval Ne'eman, nobody doubts that it is a ''fact that Lie groups have become as essential to modern theoretical physics as complex analysis and partial differential equations. DifferentialGeometry is a Maple software package which symbolically performs fun- damental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein equations, and symmetry reduction of field equations. In this section, the essence of the discussion concerning beauty and physics during the last century is exemplified by four cases: Maxwell's equations, quantum mechanics, particle physics, and the general theory of relativity. Section VIII covers Lie groups and their applications. Michael Range, FileSonic · FileServe. GTM108 Holomorphic Functions and Integral Representations in Several Complex Variables, R. To define the Lie algebra of a Lie group, we must first quickly recall some basic notions from differential geometry associated to smooth manifolds (which are not necessarily embedded in some larger Euclidean space, but instead exist .. Literature on Lie groups and Lie algebras, one uses (i), in which case the existence and basic properties of the exponential map can be provided by the Picard existence theorem from the theory of ordinary differential equations. Within this section general relativity is briefly discussed as is Noether's theorem. GTM107 Applications of Lie Groups to Differential Equations, Peter J.