Translations:The directional derivative/15/en

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Let us now introduce the important concept of a flow line. A vector field is a rule that assigns a vector to each point (x,y). An important case is the vector field defined by the gradient. In visualizing such a vector field, we imagine that the vector grad t is attached to each point. Thus, the vector field assigns a direction and a magnitude to each point. If a hypothetical particle moves in such a manner that its direction at any point coincides with the direction of the gradient at that point, then the curve traces out a so-called flow line. Because the direction of the flow line is determined uniquely by the vector field, it is impossible to have two directions at the same point. Therefore, it is impossible to have two flow lines cross each other. The contour lines and the associated flow lines are important tools in understanding seismic wave motion (Robinson and Clark, 2007[1]).

  1. Robinson, E. A., and R. D. Clark, 2007, Michael Faraday and the eikonal equation: The Leading Edge, 26, no. 1, 24–26.