*To*: mathgroup@smc.vnet.net*Subject*: [mg10765] Re: [mg10735] Need integration help!*From*: jpk@max.mpae.gwdg.de*Date*: Thu, 5 Feb 1998 00:58:15 -0500

Hi, the Set[] function evaluates its right hand side and so Your definition F[e_]=NIntegrateInterpolatingFunction[T[w]/(w^2 - e^2), {w, 1, e-1}] fails because e is not bounded to a value the solution is simple F[e_]:=NIntegrateInterpolatingFunction[T[w]/(w^2 - e^2), {w, 1, e-1}] use SetDelayed[]. Additional I recommend to restikt e to numerical values with F[e_?NumericQ]:=NIntegrateInterpolatingFunction[T[w]/(w^2 - e^2), {w, 1, e-1}] Hope that helps. Jens > I'm evaluating Mathematica on a friend's machine, trying to see if I can > do this calc so I can dump another math engine I own. I have only > Wolfram's book and my wits. > > I am calculating an integral that looks like this: > > 4 > / > | T(w)/(w^2 - 5^2) dw > / > 2 > > > It happens that T(w) is a previously defined, debugged, and well-behaved > InterpolatingFunction over the range of integration. I am using > NIntegrateInterpolatingFunction. The exact Mathematica coding I use is: > > NIntegrateInterpolatingFunction[T[w]/(w^2 - 5^2), {w, 1, 4}] > > This calculates a number. FYI, the result happens to be 0.0111 for my > T[w]. All's well so far. But, as a lead-in to my punchline question, I > am also defining a function F thusly: > > F[e_]=NIntegrateInterpolatingFunction[T[w]/(w^2 - e^2), {w, 1, 4}] > > When I define this, I get a message 'Integrand is not numerical at w = > 2.' I'm not sure what this means. I thought it was just a warning > reminder that the integrand could be singular if I wasn't careful, but > I didn't worry about it since I am making sure my value of 'e' is > always well outside of the integrating limits (in this case, e=5). But > now I realize this warning probably is serious and that I need to be > more careful because > > F[5] yields 0.0027, NOT the previous 0.0111 !!!!! > > Can anyone explain the nuances of this subtlety? What is the deep > meaning of the above warning and how can it mess me up? Am I doing > something improperly or dumb? > > > Now, if that's not enough, *here* is the -punchline- question: > > What I *really* need to do for my application is define > > F[e_]=NIntegrateInterpolatingFunction[T[w]/(w^2 - e^2), {w, 1, e-1}] > > so I can generate a list of values F[5], F[6], F[whatever]. But > Mathematica does not like the upper limit to be anything other than a > number, apparently. Regardless of my earlier question, how can I define > a function whose arguments may include an integral's upper limit? > > > Help! I'd like to switch to Mathematica. There's gotta be a way to do > this. > > > TIA > > > Stefan Jeglinski >