PHY2061 R. D. Field Department of Physics grad_1.doc Univesity of Florida Gradient of a Scalar Function Let f(x,y,z) be a scalar function of position and let zdzydyxdxrdˆˆ++=be an infinitesimal displacement vector. Directional derivative: −+++=→drzyxfdzzdyydxxfrddfdr),,(),,(lim0The directional derivative depends on the point (x,y,z) and the direction of rd. Gradient: The gradient of a scalar function f(x,y,z) is a vector whose magnitude is the maximum directional derivative at the point being considered and whose direction is the direction of
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