another simulation for this year : a equation with harmonic potential and starting with a superposition of 2 orthogonal states

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resolution of a partial differentiel equation with Crank Nicolson method : every time I have to do this , new exercice for my students, it is an opportunity to play with to create a nice simulation (here a non-homogeneous advection/transport equation )

aujourd'hui j'ai appris à faire des tresses avec grâce au package "braids"

learning the simplex method to help my daughter for her courses

I made a on the simplify_sum bug I discovered 3 weeks ago. I don't know if the problem comes from the Zeilberger/Gosper algorithm or a lack of knowledge on some special functions ....

sourceforge.net/p/maxima/bugs/

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I've just learned today that finding a closed form for the limit of some series relies on Gosper's algorithm which was first implemented in (the kernel). The algorithm reduce the problem to finding some polynomial solving a system of linear equations ...❤️

en.wikipedia.org/wiki/Gosper%2

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& c'est l'occasion de s'intéresser au modèle épidémiologique SIR simple à simuler avec ! Le plus dur est de trouver des paramètres réalistes:

➡️ γ=1/17 ~ 1/ temps de guérison
➡️ β= 0.4 ~ 1/temps inter-contaminations

On peut ensuite rendre β variable (0.4➡️ 0.1➡️ 0.2) pour simuler l'effet d'un confinement de t1 à t2=t1+2mois, on se rend compte alors que lisser le pic nécessite un confinement ni trop tôt ni trop tard! Pas simple sans connaître β,γ à l'avance...

the way to prove the formulas I gave yesterday is to study the Fourier series of the 2π periodic function equals to cos(x) on [0,π[ and 0 on [-π,0[ and apply the Dirichlet theorem to suitable x values

photos.app.goo.gl/AZXHViLWirhj

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so I've a simple closed form for the series
∑ k*sin(k*π/n)/(4*k^2-1) ( k=1 to ∞)
for all n≥2 can you guess it ?

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there was a last way to check where does the problem comes from : compute the numerical value of closed form given by and using ... so there is a bug in simplify_sum used by and !

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I also tried webapp , the closed form for the series is even more complicated , but the numerical value looks compatible with my result !

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for those who think that the problem comes from only you can check that do the same computations . But the question is why ? is the simplification false or is the numerical value of erf function at complex value i wrong?

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when I want to check such identities I try some computer algebra system like . the software often give a closed form more complicated than mine, so I compare numerical values and strange things can happend ...

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I've found these two identities while working on an examination about Fourier Series. Do you think the same formula is true when replacing the number in red by 4? If not what should be the result ?

starting my course about algorithm complexity adding a paragraph about "Pancake sorting"

un petit exemple de courbe paramétrée donnée par une équation en coordonnées polaires , étudié avec mes étudiants la semaine dernière. Pas si simple à tracer à la main, mais avec un logiciel comme on peut s'amuser à rendre le tracé plus parlant

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