Applications of Tensor AnalysisCourier Corporation, 10.06.2014 - 352 Seiten This standard work applies tensorial methods to subjects within the realm of advanced college mathematics. In its four main divisions, it explains the fundamental ideas and the notation of tensor theory; covers the geometrical treatment of tensor algebra; introduces the theory of the differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity, and hydrodynamics. Partial contents: algebraic preliminaries (notation, definitions, determinants, tensor analysis); algebraic geometry (rectilinear coordinates, the plane, the straight line, the quadric cone and the conic, systems of cones and conics, central quadrics, the general quadric, affine transformations); differential geometry (curvilinear coordinates, covariant differentiation, curves in a space, intrinsic geometry of a surface, fundamental formulae of a surface, curves on a surface); applied mathematics (dynamics of a particles, dynamics of rigid bodies, electricity and magnetism, mechanics of continuous media, special theory of relativity). |
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absolute tensors angle called Christoffel symbols cofactor common polar directions components cone conic conjugate with respect contravariant vector coordinate curves coordinate system covariant derivative covariant vector curvature curvilinear coordinates Deduce from Ex defined denote determinant differential displacement displacement vector edition equal equations of motion EXAMPLES force vector formulae function geodesic geodesic curvature given point Green's theorem h₁ h₂ Hence infinity intersection intrinsic invariant line-element linear magnitude metric tensor orthogonal particle perpendicular plane at infinity polar plane Prove quadratic form quadric quantities rectangular Cartesian referred relative tensor roots satisfies the equation skew-symmetric straight line surface symmetric tangent plane tangent vector tensor derivative tensor of weight theorem theory transformation unit vector values vanish variables velocity zero αβ δε δι диа მ ე მე მე