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grad_1 - PHY2061 R D Field Gradient of a Scalar Function...

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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 z dz y dy x dx r d ˆ ˆ + + = be an infinitesimal displacement vector. Directional derivative: + + + = dr z y x f dz z dy y dx x f r d df dr ) , , ( ) , , ( lim 0 The directional derivative depends on the point (x,y,z) and the direction of r d . 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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