How Can I plot a funcion with undefined constants??
Hi,
I'd like to know how I can plot a simple math function that has undefined constants on it. For exemple, k*x^2 - k*x^4. Here x is my variable and k is the undefined variable. This function is plottable, bacause I can plot it with my hands... You derivate the function, get the critical poits, then look at the concavite of the function in each of those points by looking at the sign of the second derivate, and then you get a plot with critical points being functions of k which I assume is always greater than zero.
From what I have found in all tutorials, books and forums, they teach only to plot numerical functions. But I can't really believe maple can't plot these functions I need. Another example would be x = k. It's a simple function where you get a horizontal line crossing the y axe in the k point. So, even if k is undefined it's still plottable. I think I made my point.
Thanks.
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- to Robert Israel:
yes,
1 hour 31 min ago - to acer:
Yes, it is
1 hour 45 min ago - I agree
1 hour 53 min ago - simpler
2 hours 6 min ago - Not that way
2 hours 25 min ago - Eigenvectors
2 hours 35 min ago - Thanks, acer,
I find another
3 hours 43 min ago - interesting idea
6 hours 45 min ago - interesting
6 hours 48 min ago - The answers
9 hours 56 min ago
Undefined constants
Yes, the basic shape may not depend on k, but the details of the plot do depend on k. In order to plot it, you need to give a value to k. So you can say something like
non-dimensionalize
As Robert Israel points out, in a Maple plot, you need to specify all parameters. If you want to see how the plot changes with parameter k, then you can plot a 3d plot, with k as one of the axes
plot3d(k*x^2 - k*x^4,x=-10..10,k=-10..10);
If a plot has a universal shape, then it can be non-dimensionalized, and the non-dimensionalized plot then encapsulates all possible behaviors. For your case of x=k, one defines the (nondimensional variable) X=x/k, and then plots X=1. For the case of y=k*x^2 - k*x^4, let Y=y/k, then Y=x^2 - x^4 has no parameters and can be plotted.
You can animate the plot.
Another way to do this is to animate the plot.
plots[animate](k*x^2 - k*x^4,x=-2..2,k=-8..8,view=[-2..2,-8..8]);
trace option for Maple 11
If you have Maple 11, you can try the option of trace in the animate command and you can have a few of the plots remain at the end of the animation. You can see this with
plots:-animate(plot,[k*x^2-k*x^4, x=-10..10],k=-5..5, trace=4);
Scott