Suppose that you had a topographical map of a piece of land and wanted to indicate at a spotP on the map the slopem of the land in a direction t. This could be done by drawing a vectormt fromP, as indicated in Fig. 4.1. Obviously, if the terrain is smooth but not level, there is one direction fromP in which the slope is a maximum. This is calledthe direction of steepest ascent.¹ The associated vector is called thegradient of the elevation atP. If you draw a contour line throughP, you will realize that the gradient atP must be ⊥ to this contour.

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Authors and Affiliations

1. Department of Applied Mathematics and Computer Science Thornton Hall, University of Virginia, Charlottesville, VA, 22901, USA

   James G. Simmonds

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