Tensor Calculus 12c The SelfAdjoint Property in Tensor Notation

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This course will eventually continue on Patreon at http://bit.ly/PavelPatreon • Textbook: http://bit.ly/ITCYTNew • Errata: http://bit.ly/ITAErrata • McConnell's classic: http://bit.ly/MCTensors • Table of Contents of http://bit.ly/ITCYTNew • Rules of the Game • Coordinate Systems and the Role of Tensor Calculus • Change of Coordinates • The Tensor Description of Euclidean Spaces • The Tensor Property • Elements of Linear Algebra in Tensor Notation • Covariant Differentiation • Determinants and the Levi-Civita Symbol • The Tensor Description of Embedded Surfaces • The Covariant Surface Derivative • Curvature • Embedded Curves • Integration and Gauss’s Theorem • The Foundations of the Calculus of Moving Surfaces • Extension to Arbitrary Tensors • Applications of the Calculus of Moving Surfaces • Index: • Absolute tensor • Affine coordinates • Arc length • Beltrami operator • Bianchi identities • Binormal of a curve • Cartesian coordinates • Christoffel symbol • Codazzi equation • Contraction theorem • Contravaraint metric tensor • Contravariant basis • Contravariant components • Contravariant metric tensor • Coordinate basis • Covariant basis • Covariant derivative • Metrinilic property • Covariant metric tensor • Covariant tensor • Curl • Curvature normal • Curvature tensor • Cuvature of a curve • Cylindrical axis • Cylindrical coordinates • Delta systems • Differentiation of vector fields • Directional derivative • Dirichlet boundary condition • Divergence • Divergence theorem • Dummy index • Einstein summation convention • Einstein tensor • Equation of a geodesic • Euclidean space • Extrinsic curvature tensor • First groundform • Fluid film equations • Frenet formulas • Gauss’s theorem • Gauss’s Theorema Egregium • Gauss–Bonnet theorem • Gauss–Codazzi equation • Gaussian curvature • Genus of a closed surface • Geodesic • Gradient • Index juggling • Inner product matrix • Intrinsic derivative • Invariant • Invariant time derivative • Jolt of a particle • Kronecker symbol • Levi-Civita symbol • Mean curvature • Metric tensor • Metrics • Minimal surface • Normal derivative • Normal velocity • Orientation of a coordinate system • Orientation preserving coordinate change • Relative invariant • Relative tensor • Repeated index • Ricci tensor • Riemann space • Riemann–Christoffel tensor • Scalar • Scalar curvature • Second groundform • Shift tensor • Stokes’ theorem • Surface divergence • Surface Laplacian • Surge of a particle • Tangential coordinate velocity • Tensor property • Theorema Egregium • Third groundform • Thomas formula • Time evolution of integrals • Torsion of a curve • Total curvature • Variant • Vector • Parallelism along a curve • Permutation symbol • Polar coordinates • Position vector • Principal curvatures • Principal normal • Quotient theorem • Radius vector • Rayleigh quotient • Rectilinear coordinates • Vector curvature normal • Vector curvature tensor • Velocity of an interface • Volume element • Voss–Weyl formula • Weingarten’s formula • Applications: Differenital Geometry, Relativity

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