Re: Linear integral along a given curve.

*To*: mathgroup at smc.vnet.net*Subject*: [mg44495] Re: Linear integral along a given curve.*From*: "Peltio" <peltio at twilight.zone>*Date*: Wed, 12 Nov 2003 08:01:46 -0500 (EST)*References*: <bk9iia$t4b$1@smc.vnet.net>*Reply-to*: "Peltio" <peltioNOSP at Miname.com.invalid>*Sender*: owner-wri-mathgroup at wolfram.com

(I am sending this again since it did not show up to the group - I've noticed that since I've changed provider I forgot to add a valid (though munged) e-mail address in reply-to, maybe that was the problem) "Jun Lin" wrote >Hi Everybody, I've just realized that I can't find any example of the >linear integral along a given or fixed curve. Does anyone have >experience of doing linear integral with Mathematica? Thanks. You might want to have a look at Bahder's "Mathematica for scientists and engineers" (a little bit outdated since it refers to version 2, but one of the best introductions to 'Mathematica thinking' I've ever read [*]). There you will find the following function LineIntegrate[ f:Literal[ _ Dt[_] | Plus[(_ Dt[_])..] ], path:{__Equal}, params:{t_,_,_}, vars:{__} ] := Integrate[ f /. First[Solve[path, vars]] /. Dt[t] -> 1, params] /; Length[path] === Length[vars] which should answer your needs as long as Solve can find a solution. For example the work made by a charge Q in the field generatet by a charge q Ef = -1/(4*Pi*e0)*q/(x^2 + y^2 + z^2)*({x, y, z}/Sqrt[x^2 + y^2 + z^2]) while moving along an elicoidal path described by the parametric equations x == Cos[u], y == Sin[u], z == 1 + 3 u/(2 Pi) 0 <= u <= 2 Pi can be found in this way: dl = Dt /@ {x, y, z}; F = Q Ef //Expand; LineIntegrate[F . dl , {x == Cos[u], y == Sin[u], z == 1 + 3*(u/(2*Pi))}, {u, 0, 2*Pi}, {x, y, z} ] cheers, Peltio invalid address in reply-to. demunging required to e-mail me [*] I wonder whether there will be a second edition. It'd be a must have.