Re: request help
- To: mathgroup at smc.vnet.net
- Subject: [mg116202] Re: request help
- From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
- Date: Sat, 5 Feb 2011 05:43:54 -0500 (EST)
- References: <iig76m$rl2$1@smc.vnet.net>
Well, I don't have an analytic approach. I just note that the plot of the function seems smooth enough that it can be easily fitted, for instance by the product of n and a polynome in r of order 4, as long as you stay out of the forbidden areas of this plot: ContourPlot[dis[r, n], {r, -1, 1}, {n, -1, 6}] So, here some fit examples: DynamicModule[{f, b, c}, f[r_, n_] := n (b r^2 + c r^4); Manipulate[ {b, c} = {b1, c1} /. FindFit[Table[{r, dis[r, n]}, {r, -0.2, 0.2, .01}], n b1 x^2 + n c1 x^4, {b1, c1}, x]; Show[ Plot[f[r, n], {r, -.2, .2}, PlotStyle -> Directive[Red, Dashed], PlotRange -> All], Plot[dis[r, n], {r, -.2, .2}, PlotRange -> All, PlotStyle -> Directive[Blue, DotDashed]] , ImageSize -> 500, Frame -> True], {n, 1, 5}, TrackedSymbols -> {n} ] ] Given the fit, the road to the inverted function is now easy and left as an exercise to the reader. Cheers -- Sjoerd On Feb 4, 7:43 am, Berihu Teklu <beri... at gmail.com> wrote: > I need to invert a real function of two real variables Dis[r, n] with > respect to the first variable r, while the second variable n is fixed. > The function is rather difficult, that I couldn't invert it. this is > kindly request you to write me any comments on the attached notebook. > > Many thanks for any help, > > Berihu > > Dis[r_, n_] := > 1/4 (2 (-2 + Sqrt[(1 + 2 n)^2]) Log[-2 + Sqrt[(1 + 2 n)^2]] - > 2 (2 + Sqrt[(1 + 2 n)^2]) Log[ > 2 + Sqrt[(1 + 2 n)^2]] - (-2 + > Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[-2 + > Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] + (2 + > Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[ > 2 + Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] - (-2 + > Sqrt[((1 + 2 n)^2 (1 + 2 n - > 2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log[-2= + > Sqrt[((1 + 2 n)^2 (1 + 2 n - > 2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]] + (2 + > Sqrt[((1 + 2 n)^2 (1 + 2 n - > 2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log[ > 2 + Sqrt[((1 + 2 n)^2 (1 + 2 n - > 2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]]) > > Solve[1/4 (2 (-2 + Sqrt[(1 + 2 n)^2]) Log[-2 + Sqrt[(1 + 2 n)^2]] - > 2 (2 + Sqrt[(1 + 2 n)^2]) Log[ > 2 + Sqrt[(1 + 2 n)^2]] - (-2 + > Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[-2 + > Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] + (2 + > Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]) Log[ > 2 + Sqrt[(1 + 2 n)^2 Cosh[2 r]^2]] - (-2 + > Sqrt[((1 + 2 n)^2 (1 + 2 n - > 2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log= [-2 + > Sqrt[((1 + 2 n)^2 (1 + 2 n - > 2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]] + (= 2 + > Sqrt[((1 + 2 n)^2 (1 + 2 n - > 2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]) Log= [ > 2 + Sqrt[((1 + 2 n)^2 (1 + 2 n - > 2 Cosh[2 r])^2)/(-2 + (1 + 2 n) Cosh[2 r])^2]]) = == > Dis[r, n], r]