       Beginner, plot with multiple rules depending on parameters

• To: mathgroup at smc.vnet.net
• Subject: [mg83739] Beginner, plot with multiple rules depending on parameters
• From: Francesco Mosconi <mosconi at pd.infn.it>
• Date: Thu, 29 Nov 2007 06:31:49 -0500 (EST)

```Hello,
I am a beginner user, and I am using Mathematica 5.0 on Windows XP. I
would like to plot a function which is composed by three rules of the form:
if x < a => F[x] = f1
if a < x < b => F[x] = f2
etc.
The thing is slightly complicated by the fact that the function rules
and the points of junction depend on several parameters and I don't know
how to evaluate them correcly. I wrote the following code:

------------------Mathematica Code--------------------------------
(*
First I clear all the variables, define the standard parameter
substitution, define some constants.
Then I define the functions of g[f],cs[f],ss[f] and sp[f].
Finally I give the rules for the function F[f,s], which is formed by
three parts, depending on the value of s.
*)

ClearAll;Clear[F];Clear[z];
stdpar = {A->50,CC->95,P->40};
kBT = 4.1;
c=kBT CC (2 Pi/3.6)^2;
p=kBT P (2 Pi/3.6)^2;
fc=kBT/A;
g[f_]:=f-Sqrt[f*fc]
cs[f_]:=c*(1-CC/(4 A)*Sqrt[fc/f])
ss[f_]:=FullSimplify[1/cs[f]*Sqrt[2 p g[f]/(1-p/cs[f])]];
sp[f_]=FullSimplify[1/p*Sqrt[2 p g[f]/(1-p/cs[f])]];
F[f_,s_]:=-g[f]+1/2 cs[f] s^2 /;s < s[f]
F[f_,s_]:=FullSimplify[-g[f]/(1-p/cs[f])+Sqrt[2 p g[f]/(1-
p/cs[f])]*s]/;ss[f]<s < sp[f]
F[f_,s_] := 1/2 p s^2 /; s > sp[f]

?F

(*
Here I just want to check that the functions of f evaluate correcly when
all the standard parameters are substituted.
*)

g/.stdpar
cs/.stdpar
ss/.stdpar
sp/.stdpar

(*
Now I would like to do the same for F, evaluating it for particular
values of f and s
*)

F[1,0.1]/.stdpar

(*
I define the function z[f,s] as minus the derivative of F with respect to f
*)

z[f_,s_]=FullSimplify[-D[F[f,s],f]]

(*
And I would like to plot it for different values of  f and s.
*)

Plot[Evaluate[Table[z[f,s],{
f,0.02,1,0.1}]/.stdpar],{s,0,0.1},PlotRange\[Rule]{-1,1}]

------------------Mathematica Code--------------------------------

I must have got sumething wrong because the function F[f,s] does not
evaluate to a number even when the /.stdpar rule is applied.
Can anyone suggest a solution?

Thank you very much

Francesco

```

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