For any of the following, click evaluate to render the image. It may take a few seconds to load. Once you see the image you may need to click again to be able to resize it by scrolling, or drag around to rotate the image. By right-clicking, you can reset the view to the first octant among other things.
Use the following to plot vector fields on \(\mathbb{R}^2\). In the second line, you may replace 'x' and 'y' with the component functions for the vector field \(\mathbf{F}(x,y) = \left< P(x,y), Q(x,y)\right>\).
Use the following to plot vector fields on \(\mathbb{R}^3\). In the second line, you may replace 'x', 'y' and 'z' with the component functions for the vector field \(\mathbf{F}(x,y,z) = \left< P(x,y,z), Q(x,y,z), R(x,y,z)\right>\).
You can use the following two boxes to plot gradient vector fields – just change 'f' to the function whose gradient vector field you wish to plot. Note that you need to place an '*' for every instance of multiplication and use '()' to denote the argument of a function. For example if we want to plot the gradient vector field of \(f(x,y) = \sin{\sqrt{xy}}\), we should write 'f = sin(sqrt(x*y))' in the sage code.