Grad[f, {x_1, ..., x_n}] gives the gradient (\[PartialD]f/\[PartialD]x_1, ..., \ \[PartialD]f/\[PartialD]x_n). Grad[f, {x_1, ..., x_n}, chart] gives the gradient in the ...

Building on Mathematica's powerful capabilities in calculus and algebra, Mathematica 9 introduces support for vector analysis. Vectors in any dimension are supported in ...

Vector analysis forms the basis of many physical and mathematical models. Mathematica can compute the basic operations of gradient, divergence, curl, and Laplacian in a ...

There are many Mathematica packages that implement symbolic mathematical operations. Here are a few examples drawn from the standard set of packages distributed with ...

As of Version 9, the functionality of the Vector Analysis Package has been integrated into the Mathematica kernel.

Other tutorials have discussed explicit loading of Mathematica packages using <<package and Needs[package]. Sometimes, however, you may want to set Mathematica up so that it ...

Laplacian[f, {x_1, ..., x_n}] gives the Laplacian \[PartialD]^2 f/\[PartialD]x_1 2 + ... + \[PartialD]^2 f/\ \[PartialD]x_n 2 . Laplacian[f, {x_1, ..., x_n}, chart] gives the ...

Some operators used in basic arithmetic and algebra. Note that the  for ∖[Cross] is distinguished by being drawn slightly smaller than the × for ∖[Times]. Interpretation of ...

Div[{f_1, ..., f_n}, {x_1, ..., x_n}] gives the divergence \[PartialD]f_1/\[PartialD]x_1 + ... + \[PartialD]f_n/\ \[PartialD]x_n. Div[{f_1, ..., f_n}, {x_1, ..., x_n}, chart] ...

Curl[{f_1, f_2}, {x_1, x_2}] gives the curl \[PartialD]f_2/\[PartialD]x_1 - \[PartialD]f_1/\[PartialD]x_2. Curl[{f_1, f_2, f_3}, {x_1, x_2, x_3}] gives the curl ...