Re: Ploting a changing constant

• To: mathgroup at smc.vnet.net
• Subject: [mg64775] Re: [mg64740] Ploting a changing constant
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 2 Mar 2006 19:27:47 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Mary Beth,

Plot allows a list of functions to plot. This can be generated by Table but
you must Evaluate the Table statement.

y[x_, a_] := a x

Plot[Table[y[x, a], {a, 10, 50, 10}] // Evaluate, {x, 0, 33}];

I would like to call 'a' a parameter and I would tend to define such a
(different) function in the following manner.

Clear[y]
y[a_][x_] := x^a

Then you can easily write the derivative of the function as...

y[2]'[x]
2 x

If you wanted to plot a series of curves with different values of a, but not
necessarily evenly spaced, then you could use MapThread. Here is an example.

Plot[MapThread[y[#][x] &, {{0, 0.2, 0.5, 1, 2, 5}}] // Evaluate, {x, 0, 1},
Frame -> True];

If you wanted to plot the derivatives then you could use...

Plot[MapThread[y[#]'[x] &, {{0, 0.2, 0.5, 1, 2, 5}}] // Evaluate, {x, 0, 1},
PlotRange -> {0, 4},
Frame -> True];

David Park

From: Mary Beth Mulcahy [mailto:Mary.Mulcahy at colorado.edu]
To: mathgroup at smc.vnet.net

OK, so this has to be an easy one.  I am trying to plot a function several
times
for a variety of values of a constant.  For example:

y[x_, a_]:=a*x

I want to plot a=10, a=20 overlaying one another.  Currently I simply
rewrite
the equation however many times I need to change the variable.  For example:

DisplayTogether[Plot[y[x, 10], {x, 0, 33}],Plot[y[x,20], {x, 0,
33}],Plot[y[x,30], {x, 0, 33}],Plot[y[x,40], {x, 0, 33}],Plot[y[50], {x, 0,
33}]]

I'm plotting this equation 15 times with a increasing in steps of ten.
Seems to
me there should be a single command to do this rather than cut and paste 10
times (and then go back in to change the variable by hand).  Something like
in
Sum[] where you can state the beginingvalue, end value and step size.

Thanks for the help.

mary beth

--
Department of Chemistry and Biochemistry