Tensors, Differential Forms, and Variational PrinciplesCourier Corporation, 01.04.1989 - 366 Seiten Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques, with large number of problems, from routine manipulative exercises to technically difficult assignments. |
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Tensors, Differential Forms, and Variational Principles David Lovelock,Hanno Rund Eingeschränkte Leseprobe - 2012 |
Häufige Begriffe und Wortgruppen
1-forms a²xi absolute differential affine connection affine tensor algebra applied arbitrary assumed ax¹ axh axk axi axh calculus of variations Christoffel symbols class C² clearly condition constitute the components construct contravariant vector coordinate system coordinate transformation corresponding covariant derivative covariant vector curvature tensor curve curvilinear coordinate defined definition denote differentiable manifold differential equations dx¹ dx² dx³ Euclidean Euler-Lagrange equations expressed exterior follows functions fundamental integral geodesic geodesic field geometry given implies indices invariant Kronecker delta Lagrangian latter linear metric tensor notation obtain orthogonal P₁ parameter problem quantities relation relative tensor represent respect right-hand side satisfied scalar density Section skew-symmetric subspace substitute symmetric tensor density tensor field theorem theory transformation law values vector field yields Σ Σ дх дхі