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Re: Log(ln) Function + 2 Parameters + Greater

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89314] Re: Log(ln) Function + 2 Parameters + Greater
  • From: "David Park" <djmpark at comcast.net>
  • Date: Thu, 5 Jun 2008 00:43:56 -0400 (EDT)
  • References: <g22tp5$ikl$1@smc.vnet.net> <g237c4$q2n$1@smc.vnet.net> <g25ntv$hug$1@smc.vnet.net>

If one considers a to be a 'parameter' and x to be the true 'variable' then 
the advantage of that form is that it is easy to write derivatives with 
respect to the variable.

f[a_][x_] := x (a + Log[x])^2

Just write the dereivative as:

f[a]'[x]

(This definition is stored under SubValues[f].)

But with the other form:

Clear[f]
f[a_, x_] := x (a + Log[x])^2

You have to write the derivative as one of the two following form:

D[f[a, x], x]
Derivative[0, 1][f][a, x]


-- 
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/


"Jerry" <Jer75811 at yahoo.com> wrote in message 
news:g25ntv$hug$1 at smc.vnet.net...
> Sir, I have never seen a function definition in the form you
> give:
> f[a_][x_] := x (a + Log[x])^2
>
> After a bit of playing with it, I don't see the difference
> between this and
>
> f[a_,x_] := x (a + Log[x])^2
>
> I really don't know how to search in help for this f[a_][x_]
> form. Can you tell me if there is any essential difference?
>
> Thank you.
>
>
> David Park wrote:
>> First, define your f function with a as a parameter.
>>
>> f[a_][x_] := x (a + Log[x])^2
>>
>> Mathematica can't make a plot unless it knows values for a. Of course, it
>> won't plot any results for x < 0 and I'm not certain if you actually 
>> meant x
>>  > 0 rather than a > 0. In any case, you can use any real domain for a. 
>> Here
>> is a plot for a specific value of a.
>>
>> Plot[f[2][x], {x, -5, 5},
>>  AxesLabel -> {x, f}]
>>
>> You can look at an extended a domain by using Plot3D.
>>
>> Plot3D[f[a][x], {a, -5, 5}, {x, 0, 5},
>>  PlotRange -> All,
>>  AxesLabel -> {a, x, f}]
>>
>> Another approach is to use a Manipulate statement with a controlled by a
>> slider.
>>
>> Manipulate[
>>  Plot[f[a][x], {x, 0, 5},
>>   PlotRange -> {0, 250},
>>   AxesLabel -> {x, f}],
>>  Style[Row[{HoldForm[f["a"][x]] == f["a"][x]}], 16],
>>  Delimiter,
>>  {a, -5, 5, Appearance -> "Labeled"}]
>>
>>
>>
> 



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