Alpha Science Int'l Ltd., Jan 1, 2005 - Mathematics - 170 pages
This work covers all the basic topics of tensor analysis in a lucid and clear language and is aimed at both the undergraduate and postgraduate in Civil, Mechanical and Aerospace Engineering and in Engineering Physics.
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Symbols of First Kind
GeodesiesRiemannian Coordinates and Geodesic Coordi
History of Tensor Calculus
Aijk Aijki arbitrary contravariant vector arbitrary tensor called Cartesian coordinate system Christoffel symbols vanish cofactor constant contravariant tensor coordinate system xl coordinates xl covariant derivative covariant differentiation covariant indices covariant tensor curvature tensor curve defined denoted dummy indices dx dx dx dxkdxi equation Euclidean space Example Exercise follows form the components functions geodesic coordinate given relation Hence independent components interchanging the dummy intrinsic derivative invariant Kronecker delta Let us consider line element metric tensor mixed tensor number of independent orthogonal partial derivatives prove quotient law reciprocal tensor rectangular Cartesian coordinate relative tensor replacing the dummy respect Rhijk Ricci tensor Riemannian metric Riemannian space Vn scalar curvature second order skew-symmetric tensor symbol of second symmetric tensor tensor Aij Tensor Calculus tensor of order tensor of rank tensor of second tensor of type Theorem travariant