Plot of vector valued function in mathematica

Mathematica
Thread starter sahon
Start date Jul 25, 2012
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Function Mathematica Plot Vector

In summary, to plot a vector valued function in Mathematica, you can use the VectorPlot3D function with three arguments: the components of the function, the range of values for the independent variables, and any other options. You can customize the appearance of the plot using various options, and plot multiple vector functions in one plot by providing a list of functions. To add labels and a legend to your vector plot, you can use the Epilog option, and animate the plot using the Animate or Manipulate functions.

Jul 25, 2012

sahon

Hi,I have vector valued function u=(u1(x,y,z),u2(x,y,z),u3(x,y,z)) and I want to plot this function in mathematica.how can I do this? I used Plot3D command but this doesn't look correct.

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Jul 25, 2012

Hepth

Gold Member

VectorPlot3D Is what you're looking for I believe.

1. How do I plot a vector valued function in Mathematica?

To plot a vector valued function in Mathematica, you can use the VectorPlot3D function. This function takes in three arguments: the components of the vector function, the range of values for the independent variables, and any other options for the plot. For example, to plot the vector function f(x,y,z) = {x^2, y^2, z^2} over the range -1<x,y,z<1, you can use the following code: VectorPlot3D[{x^2, y^2, z^2}, {-1, 1}, {-1, 1}, {-1, 1}]

2. How can I change the appearance of the vector plot in Mathematica?

You can use various options to customize the appearance of the vector plot in Mathematica. For example, you can use the VectorStyle option to change the color and style of the vectors, or the VectorScale option to adjust the length of the vectors. You can also use the PlotRange option to change the range of values shown on the plot.

3. Can I plot multiple vector valued functions in one plot in Mathematica?

Yes, you can use the VectorPlot3D function to plot multiple vector valued functions in one plot. Simply provide a list of vector functions as the first argument, and make sure the ranges for the independent variables are the same for all functions. For example, to plot the vector functions f(x,y,z) = {x^2, y^2, z^2} and g(x,y,z) = {x, y, z} over the range -1<x,y,z<1, you can use the code: VectorPlot3D[{{x^2, y^2, z^2}, {x, y, z}}, {-1, 1}, {-1, 1}, {-1, 1}]

4. How can I add labels and a legend to my vector plot in Mathematica?

You can use the Epilog option to add labels and a legend to your vector plot in Mathematica. The Epilog option allows you to specify additional graphics to be overlaid on top of the plot. For example, you can use the Text function to add labels, and the Legended function to add a legend. You can also use the PlotLabel option to add a title to your plot.

5. Is it possible to animate a vector plot in Mathematica?

Yes, you can use the Animate function in Mathematica to create an animated vector plot. This function takes in an expression to be evaluated at each frame of the animation, as well as the range of values for the animation variable. You can also use the Manipulate function to create an interactive vector plot with a slider to control the value of the animation variable.