Plotting Direction Fields with Mathamatica7

Thread starter khary23
Start date Jun 1, 2010
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Direction Fields Plotting

In summary, to plot a direction field using Mathematica7, use the StreamPlot function with two equations for dx/dt and dy/dt. You can adjust the plot size, style, and other settings using optional arguments. Multiple direction fields can be plotted on the same graph using the Show function. The appearance of the direction field arrows can be changed using the Arrowheads and ArrowStyle options. Color can be added to the direction field using the ColorFunction option. The Export function can be used to save the direction field plot as an image in various formats.

Jun 1, 2010

khary23

Can someone please explain to me how one plots direction fields of differential equations in mathamatica 7? Two examples are
y'=3-2y
y'= -1-2y

Thank you

Last edited: Jun 1, 2010

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Jun 1, 2010

jackmell

Use StreamPlot[{x'[t],y'[t]},{x,-a,a},{y,-b,b}]

and in the case of just y'=f(x,y), use:

StreamPlot[{1,f[x,y]},{x,-a,a},{y,-b,b}]

Jun 1, 2010

khary23

Thank you!

1. How do I plot a direction field using Mathematica7?

To plot a direction field using Mathematica7, you can use the StreamPlot function. This function takes in two equations, dx/dt and dy/dt, and plots the corresponding direction field. You can also adjust the plot size, style, and other settings using the optional arguments.

2. Can I plot multiple direction fields on the same graph using Mathematica7?

Yes, you can use the Show function to plot multiple direction fields on the same graph. First, use the StreamPlot function to plot the first direction field, then use the Show function to add the second direction field to the same graph. You can continue this process to add as many direction fields as you need.

3. How can I change the appearance of the direction field arrows in Mathematica7?

You can use the Arrowheads option in the StreamPlot function to adjust the appearance of the direction field arrows. This option takes in a number or a list of numbers to specify the size of the arrowheads. You can also use the ArrowStyle option to change the color and style of the arrows.

4. Is it possible to add color to the direction field in Mathematica7?

Yes, you can use the ColorFunction option in the StreamPlot function to add color to the direction field. This option takes in a function that maps values to colors. You can use built-in color functions or define your own function.

5. Can I export the direction field plot as an image in Mathematica7?

Yes, you can use the Export function to save the direction field plot as an image in various formats, such as PNG, JPEG, or SVG. You can specify the file name, format, and other options in the function. This allows you to use the direction field plot in other documents or presentations outside of Mathematica7.