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What is Del mean?
Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes the standard derivative of the function as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), it may denote any one of three operators depending on the way it is applied: the gradient or (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.
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 (or nabla) 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. These formal products do not necessarily commute with other operators or products. These three uses, detailed below, are summarized as:
Gradient: grad f = ∇ f {\displaystyle \operatorname {grad} f=\nabla f} Divergence: div v → = ∇ ⋅ v → {\displaystyle \operatorname {div} {\vec {v}}=\nabla \cdot {\vec {v}}} Curl: curl v → = ∇ × v → {\displaystyle \operatorname {curl} {\vec {v}}=\nabla \times {\vec {v}}} referencePosted on 13 Dec 2024, this text provides information on Miscellaneous in International related to International. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.
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