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Re: Solutions for functions containing jump discontinuities

• To: mathgroup at smc.vnet.net
• Subject: [mg38982] Re: Solutions for functions containing jump discontinuities
• From: atelesforos at hotmail.com (Orestis Vantzos)
• Date: Thu, 23 Jan 2003 08:05:15 -0500 (EST)
• References: <b0lvo5$5b2$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Your function simplifies to:
f[x_]:=5(x - 1500 Ceiling[x/1760])

Now assume that 
[First Case] x==1760 k + y , 0<y<=1760 and k Integer
Then Ceiling[x/1760]== Ceiling[k + y/1760]== k+1
so that f[x]==5 (-1500 + 260 k + y)

If f[x]==0 then 5 (-1500 + 260 k + y)==0 and we solve for y:
y== 1500-260 k

0<y<=1760 =>
0< 1500-260k <=1760
-1500<-260 k <= 260
5.77 > k >= 1

So k ranges from 1 to 5 and since x==1500(k+1) the roots are:
Table[1500(k + 1),{k,1,5}]
{3000, 4500, 6000, 7500, 9000}

Orestis Vantzos

newspostings at burkert.de (Burkert, Philipp) wrote in message news:<b0lvo5$5b2$1 at smc.vnet.net>...
> Hi folks,
> 
> we are searching all solutions where the function f results null. 
> 
> f[x_] := -7500 * Ceiling[(0.5 * x) / 880] + (5 * x)
> Solve[{f[x] == 0}, x]
> 
> As f contains jump discontinuities, we recieved the following error:
> 
> InverseFunction::"ifun": "Inverse functions are being used. Values may be \
> lost for multivalued inverses."
> 
> Solve::"tdep": "The equations appear to involve the variables to be solved \
> for in an essentially non-algebraic way."
> 
> We would be pleased if anybody could help us.
> 
> Regards,
> Philipp Burkert
> Carsten Siegmund

• Follow-Ups:
  • Re: Re: Solutions for functions containing jump discontinuities
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