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8

Here is the derivation promised earlier. I have chosen to create a new answer in order not to mix things up and because it shows some handling which I like to call "man-machine" interaction with Mathematica. And, sorry for the "Greeks", but I find it very cumbersome to reedit them :-( $Version "8.0 for Microsoft Windows (64-bit) (October 7, 2011)" ... 5 The problem in the posted code is that you have epsilon in place of Element. The following returns n Pi / L in both V9 and V10: u[n_, x_] := If[x <= 0 || x >= L, 0, Sqrt[2/L] Sin[n π x/L]] φ[n_, k_] := Assuming[{n ∈ Integers, L > 0}, FourierTransform[u[n, x], x, k, FourierParameters -> {0, -1}]] η[n_, k_] = Assuming[{n ∈ Integers, L > ... 4 Here is another way to get points equally spaced by chord-length. It will give a good result if the chord length is relatively small compared to the maximum radius of curvature along the curve. (If, say, the chord length is no greater than the maximum radius, then between successive points, the turning will be less 60 deg., and the difference between the ... 4 The exact analytic soultion 1. Introduction The problem was still intriguing me with the result of a further study which I present in the following, for clarity as another solution. I have chosen to write the formulas in the more theoretical text in traditonal form. Abstract We calculate here the explcit analytic solution for the integral$f(k,R)=\int ...

4

ImplicitRegion (and ParametricRegion) represent a region. They are not for plotting. Thus RegionPlot is not even remotely an alternative. You can do many operations on regions that you can look up in the documentation centre. Just a few examples: you can compute their size, decide if a point is within, compute the distance between them, find their ...

2

In mathematics, a set can be write in two(or more) form: one is {3x | x in [0,1]}, the other {x | P(x)}, where P is called a propositional function or predicate. Since Mathematica have a great power of dealing with quantifiers, once you can write a set in the second form above, you can do plenty of things and tricks that you would have thought to have ...

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