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Directional Derivatives

washam13
washam13
Directional Derivatives
Mar 30 2011, 6:21 PM EDT | Post edited: Mar 30 2011, 6:21 PM EDT
Duf = d/ds[f(x0 + su1 , y0 + su2, z0 + su3)] domain
Duf = fx(x0, y0, z0)u1 + fy(x0, y0, z0)u2 + fz(x0, y0, z0)u3
Duf = fx(x0, y0)cos(theta) + fy(x0, y0)sin(theta)

gradients
gradients are vectors
gradient f = fx i + fy j + fz k (f(x,y,z)) , gradient f = fx i + fy j - k when (z= f(x,y))

Duf = gradient f * u u is the unit vector
Duf in the direction of gradient f at P has the largest value and equals ll gradient f ll at P...... the opposite direction is the lowest value
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