partial
The partial derivative of an expression with respect to one variable.
expr(symbolic) -- e.g. x^2*y + y^3wrt(string) -- the variable, unquoted (e.g. x)
Vector Calculus
gradient
The gradient of a scalar expression as a list of partial derivatives. The list can be passed to divergence() or curl().
expr(symbolic) -- e.g. x^2*y + zcoords(string) -- the coordinate names as a list, e.g. [x, y, z]
jacobian
The Jacobian matrix of a list of expressions, as a list of rows.
field(array) -- e.g. [x*y, x + y]coords(string) -- the coordinate names as a list, e.g. [x, y, z]
hessian
The Hessian matrix (all second partial derivatives) of an expression, as a list of rows.
expr(symbolic) -- e.g. x^2*ycoords(string) -- the coordinate names as a list, e.g. [x, y, z]
divergence
The divergence of a vector field in Cartesian coordinates.
field(array) -- e.g. [x, y, z], or a bound gradientcoords(string) -- the coordinate names as a list, e.g. [x, y, z]
curl
The curl of a 3D vector field in Cartesian coordinates.
field(array) -- e.g. [y, -x, 0]coords(string) -- the coordinate names as a list, e.g. [x, y, z]
laplacian
The Laplacian of a scalar expression in Cartesian coordinates.
expr(symbolic) -- e.g. x^2 + y^2 + z^2coords(string) -- the coordinate names as a list, e.g. [x, y, z]
cylGradient
The gradient of a scalar in cylindrical coordinates (r, theta, z).
expr(symbolic) -- e.g. r^2*zr(string) -- radial coordinatetheta(string) -- azimuthz(string) -- vertical coordinate
cylDivergence
The divergence of a vector field in cylindrical coordinates.
field(array) -- components [F_r, F_theta, F_z]r(string) -- radial coordinatetheta(string) -- azimuthz(string) -- vertical coordinate
cylCurl
The curl of a vector field in cylindrical coordinates.
field(array) -- components [F_r, F_theta, F_z]r(string) -- radial coordinatetheta(string) -- azimuthz(string) -- vertical coordinate
cylLaplacian
The Laplacian of a scalar in cylindrical coordinates.
expr(symbolic) -- e.g. r^2r(string) -- radial coordinatetheta(string) -- azimuthz(string) -- vertical coordinate
cylVectorLaplacian
The vector Laplacian of a field in cylindrical coordinates.
field(array) -- components [F_r, F_theta, F_z]r(string) -- radial coordinatetheta(string) -- azimuthz(string) -- vertical coordinate
stokesTheorem
Both sides of Stokes' theorem: the line integral of F around a closed boundary curve, and the flux of curl F through a surface it bounds. The curve must be oriented with the surface's normal.
F(expression list) --coords(name list) --curve(expression list) --t(name) --t0(number) --t1(number) --surface(expression list) --u(name) --u0(number) --u1(number) --v(name) --v0(number) --v1(number) --
divergenceTheorem
Both sides of the divergence theorem: the integral of div F over a parameterized volume, and the outward flux through its boundary patches, each [[x, y, z], u, u0, u1, v, v0, v1].
F(expression list) --coords(name list) --volume(expression list) --orientation(string) -- "nonnegative" or "nonpositive"u(name) --u0(number) --u1(number) --v(name) --v0(number) --v1(number) --w(name) --w0(number) --w1(number) --patches(patch list) --