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MathGroup Archive 2005

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Re: Periodic function Roots

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58403] Re: [mg58391] Periodic function Roots
  • From: "David Park" <djmp at earthlink.net>
  • Date: Fri, 1 Jul 2005 02:01:56 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

This is also a good example for using Ted Ersek's RootSearch package on
MathSource. I believe he has just updated it, or is about to update it.
The advantage is that it will find all the roots in a domain with a single
command.

Needs["Ersek`RootSearch`"]

f[x_] := Cos[x] + .5 Cos[2x] + .25 Cos[3x] + 2.5 Cos[4x]

RootSearch[f[x] == 0, {x, 0, 2\[Pi]}]
{{x -> 0.51129}, {x -> 1.20136}, {x -> 1.91222}, {x -> 2.81887}, {x ->
      3.46432}, {x -> 4.37096}, {x -> 5.08183}, {x -> 5.7719}}

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/



From: FBellas [mailto:no at e.s]
To: mathgroup at smc.vnet.net


Hello, I'm trying to solve an periodic ecuation involving several harmonics
(Style ACos(x)+BCos(2x)+...==K). Mathematica can't let me us  'Solve'
function, so it gives me the error:
Solve::tdep: The equations appear to involve the variables to be solved for
\
in an essentially non-algebraic way.

To arrange this, i'm making a little program involving FindRoot function to
find at least two roots from the ecuation in the first period. But I would
like to know if there are some other method to do this more easily.

Thanks a lot

F. Bellas








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