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Of the integration of differential equations - Назимов P.S..

 
Название: Of the integration of differential equations
Автор: Назимов P.S..
Категория: Mathematics
Тип: The Book
Дата: 12.01.2009 14:00:05
Скачано: 4
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Описание: The first task, related to уравненИг with partial derivatives, ръчпилъ'still in 1734 Эйлеръ. In позднМшихъ своихъ сочинешяхъ онъ изсл'вдовалъ not only уравнешя of the 1-st order, but высшихъ, такъ that одинъ from методовъ решетя линейныхъ equations of the 2nd order of wear his name. Этотъ методъ впосл'Ьдствш былъ усовершенствованъ Лапласомъ, and in the такомъ Vid онъ is given in the сочиненш Грэндоржа. Этотъ способъ applies къ уравнешямъ species
t,d?I to d*z "d^z "dz ^.dz ,, " . da* dxdy , dyl dec ai
dg^ IN a, S, T, P, Q,.N-vl M- is a функцш of khnu. Онъ состоитъ in зам'ЬнЬ nepeirifflHHXb x and the other two, and v
такимъ equal, that двъ производныя втораго order *=-j and j-i
dlz t, destroyed, and there is only a derivative of the --. Бъчастномъ
the case, when in the первоначальномъ уравненш one from the production ньгхъ 2-th order not, it turns out уравнеше other form. The converted такимъ equal уравнеше Лапласъ or integrated-руетъ directly (it is then the case when the coefficients of the уравнешя satisfy the well-known conditionally), or дйлаетъ надъ этимъ уравнешемъ преобразовашя to гЬхъ поръ, while the converted уравнеше can be будетъ integrate, or find out the impossibility of интегрировашя.
At the same time with Эйлеромъ dealt with issues related to уравнешй with partial derivatives d Аламберъ, which doka-
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