Evaluation & visualization of double differentials in Mathematica

[N_F]

Hi, I'm trying to figure out how to use: http://www.wolframalpha.com/. I would like to be able to evaluate this function with different initial values and visualize results in some way, if possible:

$$d^2F = k/r^2 * i1*dl1 \times (i2*dl2 \times R)$$


Evaluate and visualize: k= 5, i1=i2= 1, r= 1, R(z)=1, dl1=dl2=?
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1. CODE: D[1] D[1] 5/1^2 * 1*{x,0,0} cross 1*{y,0,0} cross {0,-1,0}

This produces some result and it even draws some surface.



2. CODE: D[ 5/1^2 * 1*{x,0,0} cross 1*{y,0,0} cross {0,-1,0}, x,y]

I think this one gives correct result, but it does not draw anything.


EXECUTE HERE: http://www.wolframalpha.com/input/


My problem is that I have no idea what to expect, I don't know if that function produces a surface or volume, or maybe even two lines or whatever, I only know the numerical result is supposed to be either: {0,k,0} or {0,2*k,0}, which with the above initial setup equals to: {0,5,0) or {0,10,0}, but then the result can not actually be a surface but a single vector? -- If "F" has units (U), then what would be units of double differential of "F": (U/m), (U/m^2), (U*m) or (U*m^2)?

 

[jvicens]

Hi there, it looks like you are trying to evaluate and visualize the function d^2F = k/r^2 * i1*dl1 \times (i2*dl2 \times R) with different initial values. Wolfram Alpha is a powerful computational engine that can help you with this task. Here are some steps you can follow to achieve your goal:

1. Start by entering the function into the input bar on the Wolfram Alpha website. You can do this by typing or copying and pasting the function into the bar.

2. Next, add the initial values for the variables k, i1, i2, r, R, dl1, and dl2. You can do this by adding the values after the variable name with an equal sign, for example: k=5, i1=1, etc.

3. To evaluate and visualize the function, you can add the command "Plot" at the end of your input. This will generate a plot of the function with the given initial values. If you want to specify a specific range for the variables, you can use the "from" and "to" commands. For example: Plot[d^2F, {x,0,10}, {y,0,10}].

4. If you want to see the numerical result of the function, you can add the command "N" before the function. This will give you the numerical value of the function with the given initial values.

5. To see the units of the double differential of "F", you can use the command "Units" before the function. This will give you the units of the function with the given initial values.

I hope this helps you to evaluate and visualize the function using Wolfram Alpha. If you have any further questions, feel free to ask. Happy computing!