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THE FUNDAMENTAL OPERATIONS
Types of Vectors
Laws of Vector Addition
32 other sections not shown
A X B affine group assume Cartesian coordinates Cartesian orthogonal coordinates centered affine group consider constant contact manifold contravariant components coordinate lines coordinate surfaces coordinate transformations correlation tensors correspondence principle covariant base vectors covariant components covariant derivative curvature curve curvilinear coordinates cylindrical coordinates defined denote density determinant differentiation discontinuity equations of motion Euclidean space Euclidean three-space expand expressed Figure fluid follows Forming the scalar formula Further Gauss's theorem geodesic geometric Green's theorem Hence integrability conditions introduce invariant last equation last relation line integral linear manifold metric tensor normal vector obtain particle Problem properties quantities reduces result right-hand side rigid body rotation scalar product second-order tensor Section spherical coordinates symmetric tensor analysis theory tion turbulence unit vectors valid vanish vector field velocity vector verify viscosity vortex tube write