Tensor and Vector Analysis: With Applications to Differential GeometryAssuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition. |
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acceleration vector angle arc length axes boundary Calculate Christoffel symbols congruence Consider constant contravariant components coordinate system covariant components covariant derivative covariant tensor covariant vector curl defined definition denoted determinant differential equations direction cosines divergence theorem ds ds euclidean Exercise expressed F-dR field F find first first order fixed fluid follows formula Frenet-Serret formulas Gauss geodesic curvature geometry given Green’s theorem Hence indices invariant inverse jacobian line integral linear mapping metric metric tensor mixed tensor Multiply notation obtain orthogonal cartesian coordinates osculating plane parallel parameter partial derivatives path ponents principal normal quadratic radius region 3C respect result scalar scalar function scalar projection second order Section Show simple closed curve simply connected spherical coordinates surface tangent plane three-space tion union curves unit normal unit vector variables vector field vector with components velocity vector zero