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Curl

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Curl[{f1, f2}, {x1, x2}]

gives the scalar curl D[f2,x1] - D[f1,x2].

Curl[{f1, f2, f3}, {x1, x2, x3}]

gives the vector curl (D[f3,x2]-D[f2,x3], D[f1,x3]-D[f3,x1], D[f2,x1]-D[f1,x2]). For an n*n*...*n array the generalized Levi-Civita curl (depth n-k-1) is returned.

Curl[f, {x1, ..., xn}, chart]

gives the curl of a vector field in the orthonormal basis of chart ("Cartesian", "Polar", "Cylindrical", "Spherical").

Examples (8)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (8)

In[1]:= Grad[Sin[x^2 + y^2], {x, y}]
Out[1]= {2 x Cos[x^2 + y^2], 2 y Cos[x^2 + y^2]}

In[2]:= Grad[{x y, y z, z x}, {x, y, z}]
Out[2]= {{y, x, 0}, {0, z, y}, {z, 0, x}}

In[3]:= Div[{x^2, y^2, z^2}, {x, y, z}]
Out[3]= 2 x + 2 y + 2 z

In[4]:= Curl[{y, -x}, {x, y}]
Out[4]= -2

In[5]:= Laplacian[x^2 + y^2 + z^2, {x, y, z}]
Out[5]= 6

In[6]:= Div[{r Sin[t], -r Cos[t]}, {r, t}, "Polar"]
Out[6]= 3 Sin[t]

In[7]:= -Grad[k q/r, {r, t, p}, "Spherical"]
Out[7]= {(k q)/r^2, 0, 0}

In[8]:= Laplacian[Sin[r^2], {r, t}, "Polar"] // Simplify
Out[8]= 4 - 4 r^2

Implementation notes

Attributes: Protected.

References

See also: Grad, Div, Laplacian, D