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There is no mechanism to work automatically on real variables only in a whole notebook. You must explicitly declare which variables are real, for example with `$Assumptions`: $Assumptions = Element[x | y, Reals] && z >= 0
To avoid premature evaluation of `pselect` you can give a numerical pattern for `cindices`: pselect[A_, lenA_, cindices : {__Integer}]:= Product[A[[r, cindices[[r]]]], {r, 1, lenA}];
My old package `CurvesGraphics6` was motivated precisely by this kind of problems. You can download it from https://www.dimi.uniud.it/gorni/Mma
To eliminate the square I am afraid you will need to go to a triple integral: Integrate[Integrate[f[s, u], {u, 0, s}]^2, {s, 0, T}] == Integrate[Integrate[f[s, u], {u, 0, s}]* Integrate[f[s, v], {v, 0, s}], {s, 0, T}] == ...
I am glad you appreciated my help!
It is Fubini's theorem, hoping that your functions are bounded: Integrate[f[s] Integrate[g[u], {u, 0, s}], {s, 0, T}] == Integrate[Integrate[f[s] g[u], {u, 0, s}], {s, 0, T}] == Integrate[f[s] g[u], {u, 0, s}, {s, 0, T}] == ...
This may be a start: Manipulate[ StreamPlot[{x^2 + y + x y, -((363889 x)/5000) - 10 x^2 + (3 y)/ 2000 + (11 x y)/5 + (7 y^2)/10}, {x, -k, k}, {y, -9 k, 9 k}, StreamScale -> None, StreamPoints -> Fine], {k, .1, 20}]
With some Mathematica knowledge you can do whatever: Graphics[ Map[{Thickness[RandomReal[{.001, .05}]], Arrowheads[(#[[1, 1]] + #[[2, 2]])/10], RandomColor[], Arrow[{#[[1]], #[[1]] + #[[2]]}]} &, {{{0, 1}, {1, 1}},...
Ok, try with `3/2+1/5`: In[17]:= xxxx /. {me -> 1, Te -> 1, \[Omega]pe -> 1, \[Omega]ce -> 1, ky -> 1, \[Epsilon]b -> 1, c -> 1, k -> 1, kpar -> 1, kz -> 1, \[Omega]pi -> 1, vde -> 1, \[Kappa] -> 3/2 + 1/5,...
There are many problems with your code. There is a lowercase `which`. Anyway, you should use `Piecewise`, and not `Which`, for symbolic math. The equation v[k]'[t] == (i[k][t] - i[k + 1][t])/Cv[k][t] involves `i[k+1]`. When `k` ranges...