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RE: Making plots using transformation rules
*To*: mathgroup at smc.vnet.net
*Subject*: [mg71951] RE: [mg71928] Making plots using transformation rules
*From*: "David Park" <djmp at earthlink.net>
*Date*: Tue, 5 Dec 2006 06:04:56 -0500 (EST)
Why do you use a SetDelayed instead of a simple Set?
g[t_] = D[t^2, t]
2 t
Plot[g[t], {t, 0, 10}];
Or if you had some more complicated function with parameters you might
define it with subvalue parameters as follows:
f[a_, b_][t_] = D[a t^3 + b Sin[t], t]
3*a*t^2 + b*Cos[t]
Plot[f[2, 300][t], {t, 0, 10}];
Or you could even use
h[a_, b_][t_] := a t^3 + b Sin[t]
Plot[h[2, 300]'[t], {t, 0, 10}];
It is generally worthwhile to have a function that is going to be plotted
well defined before plugging it into a Plot command - as opposed to doing a
lot of processing within the Plot command.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: amannuc at yahoo.com [mailto:amannuc at yahoo.com]
I've read about making plots of functions, for example:
Plot[Evaluate[f[x]], {x, 0, 10}]
I don't have this sort of function to plot. Because it involves
derivatives, I only get numerical output after defining a
transformation rule. A simple example (not the real one) is the
following:
g[t_] := D[t^2, t]
g[t] /. t -> 1
I cannot evaluate g[1], because then Mathematica thinks I am trying to
take a derivative with respect to the number 1, and flags that as
error. So I need the transformation rule to get function values.
What is the best way to plot g[t]? I am looking to create multiple
transformation rules that replace the argument t with a reasonable
range of values. Then I can plot g[t] versus t. Plot will not do this
directly because it takes variable values as input. However, as I've
said, the construction g[x] (x = some number) flags an error.
Thanks for your help.
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