The Gradient(f(x, y,...), [x, y,...] = [a1, b1,...]) calling sequence returns the gradient of the function f at specified points. Multiple points can be given by putting them into a list, for example, Gradient(f(x,y), [x,y] = [[1,2],[2,0]]). In the case of a function of 2 variables, the output option can be used to request that a plot or gradplot be returned.

The Del and Nabla commands are both aliases for the Gradient command.

The GradientTutor routine offers equivalent capabilities to Gradient in a tutor interface.  See the Student[MultivariateCalculus][GradientTutor] help page.

If output=plot is given (so in particular, the function expression has at most two variables), the opts argument can be used to control the appearance of the plot.

caption = string

Specifies the plot or gradplot caption.  The default caption is constructed from the parameters.

functionoptions = list

Specifies the plot options for plotting the function $f\left(x\,y\right)$. For more information on plotting options, see plot3d/options.

curveoptions = list

Specifies the plot options for plotting the level curve of the function at the point where the gradient is computed, and its projection on the x-y plane. For more information on plotting options, see plot3d/options.

gradientoptions = list

Specifies the plot options for plotting the gradient of the function. For more information on plotting options, see plot3d/options.

output = value, plot, or gradplot

This option controls the return value of the function.

* output = value specifies that the value of the gradient is to be returned. Plot options are ignored if output = value.  The default is output = value.

* output = plot specifies that a plot displays, which shows the function, a level curve at the point, the projection of that level curve onto the x-y plane, and a scaled vector in the direction of the gradient.

* output = gradplot specifies that a gradplot displays.

gradplotoptions = list

Specifies the plot options if the output is a gradplot. For more information on plotting options, see plot/options.

showfunction = true or false

Determines whether the function $f\left(x\,y\right)$ is plotted. The default is true.

showcurves = true or false

Determines whether the level curve is plotted. The default is true.

showprojectedcurves = true or false

Determines whether the projection of the level curve is plotted; this option is ignored if showcurves is false. The default is true.

For more information on typesetting the title or caption, see plot/typesetting.

title = anything

A title for the plot.

The default title is constructed from the parameters and the command options. title = "" disables the default title. For more information about specifying a title, see plot/typesetting.

caption = anything

A caption for the plot.

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption, see plot/typesetting.

view = list

Specifies the plot or gradplot view.  

For information on how to change the default colors, see the Student[SetColors] help page.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\right)\:$

$\mathrm{Gradient}\left(x^2+y^2,\left[x\,y\right]=\left[0\,1\right]\right)$

$\left[\left[\begin{array}{c}0\\ 2\end{array}\right]\right]$

$\mathrm{Del}\left(x^2+y^2\,\left[x\,y\right]=\left[0\,1\right]\right)$

$\left[\left[\begin{array}{c}0\\ 2\end{array}\right]\right]$

$\nabla \left(x^2+y^2\,\left[x\,y\right]=\left[0\,1\right]\right)$

$\left[\left[\begin{array}{c}0\\ 2\end{array}\right]\right]$

$\mathrm{Gradient}\left(x^2+y^2,\left[x\,y\right]=\left[\left[0\,1\right]\,\left[2\,1\right]\right]\right)$

$\left[\left[\begin{array}{c}0\\ 2\end{array}\right]\,\left[\begin{array}{c}4\\ 2\end{array}\right]\right]$

$\mathrm{Gradient}\left(x^2+y^2,\left[x\,y\right]=\left[\left[0\,1\right]\,\left[2\,1\right]\right],\mathrm{output}=\mathrm{gradplot}\right)$

$\mathrm{Gradient}\left(x^2+y^2,\left[x\,y\right]=\left[\left[0\,1\right]\,\left[2\,1\right]\right],x=-1..6,y=-1..6,z=0..10,\mathrm{output}=\mathrm{plot}\right)$

The curveoptions, showcurves and showprojectedcurves options were introduced in Maple 17.

For more information on Maple 17 changes, see Updates in Maple 17.