Wronskian oor Fins

Wronskian

naamwoord

a determinant that is used in the study of differential equations, and can sometimes be used to show that a set of solutions is linearly independent.

Vertalings in die woordeboek Engels - Fins

Wronskin determinantti

voorbeelde

The Wronskian of two differentiable functions f and g is W(f, g) = f g′ – g f ′.
Kahden funktion f ja g Wronskin determinantti on W(f, g) = fg′ – gf ′.

A common misconception is that W = 0 everywhere implies linear dependence, but Peano (1889) pointed out that the functions x2 and |x|x have continuous derivatives and their Wronskian vanishes everywhere, yet they are not linearly dependent in any neighborhood of 0.
Giuseppe Peano painotti kuitenkin jo varhain (1889), että on olemassa funktioita kuten x2 ja |x|x, joilla on jatkuvat derivaatat ja joiden Wronskin determinanttien arvot ovat 0 kaikilla x:n arvoilla, ja silti niiden muodostama funktiojono ei ole lineaarisesti riippuva.

Moreover, it is illustrated that a q-Casorati determinant plays a similar role in the theory of linear q-difference equations as a Wronskian determinant in the theory of linear differential equations.
Lisäksi osoitetaan, että q-Casoratin determinantilla on samantapainen rooli lineaaristen q-differenssiyhtälöiden teoriassa kuin Wronskin determinantilla on differentiaaliyhtälöiden teoriassa.

In mathematics, the Wronskian (or Wrońskian) is a determinant introduced by Józef Hoene-Wroński (1812) and named by Thomas Muir (1882, Chapter XVIII).
Matematiikassa Wronskin determinantilla tarkoitetaan determinanttia, jonka kehitti Józef Maria Hoene-Wroński ja nimesi Thomas Muir.