Abstract
Suppose that you had a topographical map of a piece of land and wanted to indicate at a spot P on the map the slope m of the land in a direction t. This could be done by drawing a vector m t from P, as indicated in Fig. 4.1. Obviously, if the terrain is smooth but not level, there is one direction from P in which the slope is a maximum. This is called the direction of steepest ascent.1 The associated vector is called the gradient of the elevation at P. If you draw a contour line through P, you will realize that the gradient at P must be ⊥ to this contour.
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© 1982 Springer-Verlag New York Inc.
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Simmonds, J.G. (1982). The Gradient Operator, Covariant Differentiation, and the Divergence Theorem. In: A Brief on Tensor Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0141-7_4
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DOI: https://doi.org/10.1007/978-1-4684-0141-7_4
Publisher Name: Springer, New York, NY
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