Vector and Tensor Analysis- frikilife.comnko frikilife.comNewYork: Dover Publications, This book not only comprises the standard vector analysis of Gibbs, including dyadics or tensors of valence two, but also supplies an introduction to the algebra of motors, which is apparently destined to play an important role in mechanics as well as in line geometry. The entire theory is illustrated by many significant applications; Cambridge University Press, Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach
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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.
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