Vector functions {gradient, vector}| can be sum of each partial derivative times its unit vector i: (Df(x,y) / Dx) * i + (Df(x,y) / Dy) * j, where D is partial derivative. Gradient is in respect to direction. Gradient uses an operator {del operator}, which is upside-down uppercase delta: del = ((D / Dx) * i + (D / Dy) * j). For two dimensions, gradient is normal vector to vector-function curve. For three dimensions, gradient is normal vector to vector-function surface.
Vector functions {curl, vector}| can be vector products of del operator and vector function: del x f. Curl of gradient of scalar function equals zero: del x (del f) = 0.
Scalar functions {divergence, vector}| can be scalar products of del operator and vector function: del . f. Divergence of curl equals zero: del . (del x f) = 0.
3-Calculus-Differentiation-Function
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Date Modified: 2022.0225