Symbol des Eheringzitats

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When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field a function defined on a multi-dimensional domain , it may denote the gradient locally steepest slope of a scalar field or sometimes of a vector field , as in the Navier—Stokes equations , the divergence of a vector field, or the curl rotation of a vector field, depending on the way it is applied. Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product with a scalar, a dot product , and a cross product , respectively, of the del "operator" with the field.

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The nabla is a triangular symbol like an inverted Greek delta: After receiving Smith's suggestion, Tait and James Clerk Maxwell referred to the operator as nabla in their extensive private correspondence; most of these references are of a humorous character. It was probably this reluctance on the part of Maxwell to use the term Nabla in serious writings which prevented Tait from introducing the word earlier than he did. The one published use of the word by Maxwell is in the title to his humorous Tyndallic Ode, which is dedicated to the "Chief Musician upon Nabla," that is, Tait. William Thomson Lord Kelvin introduced the term to an American audience in an lecture; [2] the notes were published in Britain and the U.

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