Applied Mathematics 1413 Chapter Notes - Chapter 12.5: Directional Derivative, Level Set
1 Jan 2019
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Document Summary
If is differentiable @ the point and , then is a normal vector to the level curve of that pases through. @ , increases most rapidly in the direction of the gradient vector. @ , decreses most rapidly in the direction. The rate of change of @ is zero in directions tangent to the level curve of that passes through. The directional derivative of @ in the direction of a unit vector ( ) is the rate of change of with respect to distance measured @ along a ray. Partial differentiation page 1 is the rate of change of with respect to distance measured @ along a ray in the direction of in the -plane. If is differenitable @ and , then the directional derivative of @ in the direction of is given by: The rate of change of @ as measured by an observer moving through with velocity is unit of per unit time.
