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Change of Coordinates

In: Introduction to Tensor Analysis and the Calculus of Moving Surfaces

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  • Pavel Grinfeld

    (Drexel University, Department of Mathematics)

Abstract

Tensor calculus achieves invariance by establishing rules for forming expressions that evaluate to the same value in all coordinate systems. In order to construct expressions that do not depend on the choice of coordinates, one must understand how individual elements transform under a change of coordinate. This chapter is therefore devoted to the study of coordinate changes and the corresponding changes in calculated quantities. Looking ahead, we discover that certain objects transform according to a special rule that makes it particularly easy to form invariant combinations. Such objects are called tensors.

Suggested Citation

  • Pavel Grinfeld, 2013. "Change of Coordinates," Springer Books, in: Introduction to Tensor Analysis and the Calculus of Moving Surfaces, edition 127, chapter 0, pages 35-51, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7867-6_4
    DOI: 10.1007/978-1-4614-7867-6_4
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