Surface integrals

Surface integrals accumulate scalar densities or oriented flux over a surface.

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Double and triple integrals
Integration over planar or spatial regions accumulates density into total quantities.
Jacobian matrix
The derivative matrix of a multivariable map captures its local linear action.
Antiderivatives
An antiderivative has the given function as its derivative; on an interval, any two antiderivatives differ by a constant.
Chain rule
The derivative of a differentiable composition combines the derivative of the outer function with that of the inner function.
Change of variables
A suitable coordinate change transforms volume elements through the absolute Jacobian determinant.