a function, usually expressed as a polynomial, that indicates linear combinations of the derivatives of the expression on which it operates.
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British Dictionary definitions for differential operator
any operator involving differentiation, such as the mathematical operator del ∇, used in vector analysis, where ∇ = i ∂/∂ x + j ∂/∂ y + k ∂/∂ z, i, j, and k being unit vectors and ∂/∂ x, ∂/∂ y, and ∂/∂ z the partial derivatives of a function in x, y, and z
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012