Vector and tensor analysis - Louis Brand - Google книгиIn 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. Developed by Gregorio Ricci-Curbastro and his student Tullio Levi-Civita ,  it was used by Albert Einstein to develop his theory of general relativity. 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 and quantum field theory. Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern 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.
Vector and Tensor Analysis, Second Edition
Surface Geometry. Orthogonal Transformations! Motor Identities. Mathematical Physics.You may send this item to up to five recipients. Doublets and Double Layers. The solved problems are difficult and are worked out in great detail? However, formatting rules can vary widely between applications and fields of interest or study.
Irrotational Vectors. Minimal Surfaces. The Affine Group. Line Integrals?
Absolute Tensors. Great Circle Arcs. Working with a main proponent of the exterior calculus Elie Cartan, the influential geometer Shiing-Shen Chern summarizes the role of tensor calculus: . Tensor Analysis article page The Summation Convention.
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You may send this item to up to five recipients. An oldie-but-goodie with much the same nature as the present book is G. Steady Motion! Please verify that you are not a robot. Preview this Book.
Vector and tensor analysis. Louis Brand. Addition of Vectors. Subtraction of Vectors. Multiplication of Vectors by Numbers. Linear Dependence. Collinear Points.
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Borisenko and I. The J matrix representing the change from unbarred to barred coordinates. Mean value theorem Rolle's theorem. Components of a Vector.Euclidean Geometry. The Affine Group. Your request to send this item has been completed. Irrotational Motion.
Euclidean Geometry. In some cases they extend the discussion in vectot text. There are also little examples scattered through the text, but most of these just point out that some physical quantity is a tensor without telling you how this information is useful. Space Charges.