Re: DiscretePlot

*To*: mathgroup at smc.vnet.net*Subject*: [mg96773] Re: [mg96697] DiscretePlot*From*: peter <plindsay.0 at gmail.com>*Date*: Tue, 24 Feb 2009 05:47:46 -0500 (EST)*References*: <200902220038.TAA08394@smc.vnet.net>

well, I'm sure its all explained in the manual.... 2009/2/22 Helen Read <hpr at together.net>: > I recently started the chapter on series in my Calculus II classes. I > like to have my students make tables and plots of terms and partial sums > of series, to help them develop some intuition about what it means for a > series to converge or diverge, which leads naturally into convergence > tests. (Give them something where it's hard to determine > convergence/divergence from tables and plots, and the students will > *ask* how can we know for sure.) Prior to Mathematica 7, we always had > to start with a table, name it something, and use ListPlot to plot it. > So now with Mathematica 7, I still have my students make some smallish > tables (I like them to have numbers to look at it in addition to plots), > but now we can plot directly with the new DiscretePlot. I like > DiscretePlot a lot, except for one complaint I will get to below. > > As an example, consider the alternating harmonic series. My students > know how to define a function for the terms and a function to generate > the partial sums, then plot the terms or the partial sums with > DiscretePlot, like so. > > a[n_] = (-1)^(n + 1)/n > > s[k_] := Sum[a[n], {n, 1, k}] > > DiscretePlot[s[k], {k, 1, 100},PlotLabel->"Partial sums"] > > We can turn off the filling. (I like the filling sometimes, but not always.) > > DiscretePlot[s[k], {k, 1, 100}, Filling -> None] > > All well and good. > > However, unlike ListPlot (which has Joined->False by default), > DiscretePlot has Joined->Automatic by default. If we plot greater than > 149 points with DiscretePlot, Mathematica joins the points, and it's a > royal mess. > > DiscretePlot[s[k], {k, 1, 149}, Filling -> None] (* this is fine *) > > > DiscretePlot[s[k], {k, 1, 150}, Filling -> None] (* this is a wreck *) > > As another example, try using DiscretePlot to plot terms of the sequence > b(n)=sin(n). > > b[n_] = Sin[n]; > DiscretePlot[b[n], {n, 0, 500}, Filling -> None] > > Well that's just hideous. Students just learning about sequences and > series aren't going to have any idea what's going on. > > We can fix this behavior by setting Joined->False, like this: > > DiscretePlot[s[k], {k, 1, 150}, Filling -> None, Joined -> False] > > DiscretePlot[b[n], {n, 0, 500}, Filling -> None, Joined -> False] > > The students are having trouble remembering to do this, though, and I > wonder why on earth Wolfram would design DiscretePlot this way. When I > go to make a DiscretePlot, I do not *ever* expect -- or want -- the > points to be joined. And why are the points not joined for < 150 points, > and joined for >= 150 points? This seems completely arbitrary, and in > fact I only discovered the 150 point cut-off by trial and error, and > could find no explanation in the Documention as to what > Joined->Automatic even does. > > I'd be far happier if DiscretePlot had Joined->False by default. > > -- > Helen Read > University of Vermont > > >

**References**:**DiscretePlot***From:*Helen Read <hpr@together.net>

**Re: Error using Manpulate that is NOT obvious (to me)**

**Re: Error using Manpulate that is NOT obvious (to me)**

**DiscretePlot**

**Re: DiscretePlot**