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Re: variables versus functions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg28808] Re: variables versus functions
*From*: "Orestis Vantzos" <atelesforos at hotmail.com>
*Date*: Mon, 14 May 2001 01:33:00 -0400 (EDT)
*Organization*: National Technical University of Athens, Greece
*References*: <9dld6m$o9g@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Well A=Cos[x] will always be the Cosinus of x, whereas A[x_]:=Cos[x] is the
abstract concept of Cosinus, so that A[t]=Cos[t],A[2]=Cos[2] etc.
FindRoot[A==B,...] would simply not work since A[x_]:=Cos[x] does not mess
around with the symbol A itself (A will still evaluate to A, not Cos[...]).
FindRoot[A[x]==B[x],{x,pi/2}] would work like a charm though...and so would
FindRoot[A[t]==B[t],{t,pi/2}] which takes us back to your first question.
Orestis
PS. You can think of A=Cos[x] as an EXPRESSION (something that simply is),
whereas A[x_]:=Cos[x] defines a FUNCTION (something that does something).
"Julian Sweet" <jsweet at engineering.ucsb.edu> wrote in message
news:9dld6m$o9g at smc.vnet.net...
> How is it different to define a variable such as A=Cos[x]
> versus a function A[x_]:=Cos[x] ?
>
> Furthermore, what If I define two functions A[x_]:=Cos[x] and
> B[x_]=ArcTan[x]? How would FindRoot[A==B,{x,pi/2}] treat this
> differently than if I just used variable definitions for A & B?
>
>
> e-mail response appreciated: jsweet at engineering.ucsb.edu
>
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