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for example, the function:formula_12is infinitely differentiable at , and has all derivatives zero there.
Για παράδειγμα η συνάρτηση:formula_13είναι απείρως παραγωγίσιμη στο και όλες οι παράγωγοι είναι μηδέν στο σημείο.
Última atualização: 2016-03-03
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it is known that there exists no c2 (twice continuously differentiable) embedding of a flat torus into 3-space.
it is known that there exists no c2 (twice continuously differentiable) embedding of a flat torus into 3-space.
Última atualização: 2016-03-03
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===lie theory===a lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.
=== Η Θεωρία του lie ===Μια lie ομάδα είναι μια ομάδα η οποία είναι επίσης διαφορίσιμη πολλαπλότητα, με την ιδιότητα ότι οι λειτουργίες της ομάδας είναι συμβιβαστή με την ομαλή δομή.
Última atualização: 2016-03-03
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consider a sawtooth wave:formula_11:formula_12in this case, the fourier coefficients are given by:formula_13it can be proven that the fourier series converges to "s"("x") at every point "x" where "s" is differentiable, and therefore:{n} \sin(nx), \quad \mathrm{for} \quad x - \pi \notin 2 \pi \mathbf{z}.
Σκεφτείτε ένα πριονωτό κύμα:formula_14:formula_15Στην περίπτωση αυτή, οι συντελεστές fourier δίνονται από:formula_16Μπορεί να αποδειχθεί ότι η σειρά fourier συγκλίνει στο s (x) σε κάθε σημείο x όπου α είναι διαφορίσιμη, και ως εκ τούτου: :{n} \sin(nx), \quad \mathrm{for} \quad x - \pi \notin 2 \pi \mathbf{z}.
Última atualização: 2016-03-03
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