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Coordinate Systems and the Role of Tensor Calculus

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 was invented in order to make geometric and analytical methods work together effectively. While geometry is one of the oldest and most developed branches of mathematics, coordinate systems are relatively new, dating back to the 1600s. The introduction of coordinate systems enabled the use of algebraic methods in geometry and eventually led to the development of calculus. However, along with their tremendous power, coordinate systems present a number of potential pitfalls, which soon became apparent. Tensor calculus arose as a mechanism for overcoming these pitfalls. In this chapter, we discuss coordinate systems, the advantages and disadvantages of their use, and explain the need for tensor calculus.

Suggested Citation

  • Pavel Grinfeld, 2013. "Coordinate Systems and the Role of Tensor Calculus," Springer Books, in: Introduction to Tensor Analysis and the Calculus of Moving Surfaces, edition 127, chapter 0, pages 21-34, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7867-6_3
    DOI: 10.1007/978-1-4614-7867-6_3
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