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Vectors, Pure and Applied by T. W. Körner

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9

Cartesian tensors

9.1 Physical vectors

When we discussed the use of vectors in geometry, I did not set up the axioms of geometry, but appealed to the reader’s knowledge and intuition concerning planes and lines. It is useful and instructive to see how Euclidean geometry can be developed from axioms, but it would have taken us far away from our main topic.

In the next two chapters we shall develop the idea of a Cartesian tensor. Cartesian tensors are mainly used in physics, so we shall encounter ‘point masses’, ‘smoothly varying functions of position’ and similar slightly louche characters. In addition, matters which would be made explicit by a pure mathematician will be allowed to remain implicit. Repeated trials have shown that it is rarely ...

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