Ask for help with Divergence in Derive 6

In summary, The user is experiencing issues with the divergence function DIV in DERIVE 6. They have loaded the utility "VectorMatrixFunctions.mth" and when inserting a specific vector, they are getting a result of zero. However, the user believes this is incorrect and expects a non-zero value based on the poisson equation for gravity. The conversation then discusses possible errors in the user's calculations and suggests that DERIVE may be expecting the vector in cartesian form. Finally, several examples of DIV calculations are provided.
  • #1
pogono
1
0
Hello,
I have a problem with divergence function DIV in DERIVE 6 and canot find anything in help and web forums either.

#1. At first, I load utility "VectorMatrixFunctions.mth"

#2. when I insert DIV([1/r^2, 0, 0], spherical) I obtain ZERO

But it seems wrong,
f.e. for Gravitation we have divergence for vectors with (1/r^2) and we should expect poisson equation related to volume,
As we know for gravity it is (4 \pi GMm ) / V

What is wrong then with my calculations using Derive 6?
 
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  • #2
DIV([r,s,t]) gives 0
DIV([x,y,z]) gives 3

so perhaps Derive is expecting your vector in [x,y,z] cartesian form.

DIV([1/x^2,0,0]) gives -2/x^3
DIV([1/(x^2+y^2+z^2),0,0]) gives - 2*x/(x^2 + y^2 + z^2)^2
 
Last edited:

1. What is Divergence in Derive 6?

Divergence in Derive 6 is a mathematical concept that measures the rate of change of a vector field at a given point. It can also be thought of as a measure of how much a vector field is spreading out or converging at a particular point.

2. How can I calculate Divergence in Derive 6?

To calculate Divergence in Derive 6, you can use the built-in function "div" and input the vector field you want to calculate at a specific point. For example, if you want to calculate the divergence of the vector field F(x,y)= 2x + 3y at the point (3,4), you can type in the command div(2x+3y, 3, 4) and the result will be returned.

3. How can I graph Divergence in Derive 6?

To graph Divergence in Derive 6, you can use the "VectorField" command to plot the vector field and then use the "Gradient" command to plot the divergence as a contour plot. You can also use the "StreamPlot" command to visualize the vector field and the "Divergence" command to plot the divergence as a color map.

4. Can I use Divergence in Derive 6 for 3-dimensional vector fields?

Yes, you can use Divergence in Derive 6 for 3-dimensional vector fields by using the "divergence" command and inputting the vector field in the form of divergence([Fx,Fy,Fz], x, y, z). This will return the divergence of the vector field at a specific point in 3-dimensional space.

5. How can I use Divergence in Derive 6 for real-life applications?

Divergence in Derive 6 has many real-life applications in fields such as physics, engineering, and fluid mechanics. It can be used to model fluid flow, electric and magnetic fields, and optimize designs for various systems. It is also used in the study of heat transfer, seismology, and meteorology. By understanding and calculating divergence, we can gain insights into the behavior of various systems and make informed decisions in real-world situations.

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