Tensor calculus: a concise course
In mathematics , tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields tensors that may vary over a manifold , e. Contrasted with the infinitesimal calculus, tensor calculus allows presentation of physics equations in a form that is independent of the choice of coordinates on the manifold. Tensor calculus has many real-life applications in physics and engineering , including elasticity , continuum mechanics , electromagnetism see mathematical descriptions of the electromagnetic field , general relativity see mathematics of general relativity , quantum field theory. Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern nicely summarizes the role of tensor calculus . In our subject of differential geometry, where you talk about manifolds, one difficulty is that the geometry is described by coordinates, but the coordinates do not have meaning. They are allowed to undergo transformation.
View Full Version : A work book in Tensors. I am looking to get a book that I can work through in Tensors. I am considering getting one or two of the following please see links below. I need there to be worked problems or proofs so that I can get a real understanding. I have done a Physics degree. But I have had to revise pretty well all the math.
Barry Spain Tensor Calculus Oliver & Boyd Acrobat 7 Pdf Mb. Scanned by artmisa using Canon DRC + flatbed option.
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Tensor Calculus for Physics Ep. 9 - Derivatives of Tensors, and the Affine Connection
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