Txawv sib npaug - General Information thiab Scope

Kawm tshwm sim ntawm qhov, daws ntau yam kev pab raws qib nyob rau hauv kev lag luam, biology, physics, engineering, tsis yog ib txwm tau mus sai li sai tau tsim kom muaj ib tug ncaj qha kev txuas ntawm los ntawm ib co tseem ceeb uas hais txog ib tug evolutionary txheej txheem. Feem ntau, ib tug yuav txiav txim seb lub kev sib raug zoo ntawm cov kev ntseeg (functions) thiab lawv tus nqi ntawm kev hloov nrog rau kev hwm mus rau lwm yam (sab nraud) nce mus nce los. Qhov no seb puas tsimnyog tau sib npaug nyob rau hauv uas tus tsis paub zog yog nyob rau hauv lub kos npe rau ntawm lub derivative - ib tug txawv kab zauv. Nyob rau hauv lawv txoj kev tshawb no peb siv ib tug ntau lub sij hawm, ib tug ntau ntawm nto moo kws tshawb fawb: Newton, Bernoulli, Laplace thiab lwm tus neeg. Kev siv cov differential sib npaug yog lug: cov qauv ntawm cov nyiaj txiag muaj zog, displaying tsis tau tsuas yog cov nyob nce mus nce los nyob rau hauv lub sij hawm, tab sis kuj lawv kev sib raug zoo nrog lub sij hawm, nyob rau hauv cov teeb meem ntawm micro- thiab macroeconomics; siv kom lawv qhia lub propagation ntawm electromagnetic thiab tshav kub tsis, thiab ntau yam evolutionary phenomena uas tshwm sim nyob rau hauv nyob thiab uas tsis yog-nyob xwm.

Nrog kev pab los ntawm electromagnetic vuag mus rau kis ntaub ntawv ntawm ib tug deb (TV, xov tooj, xov tooj cua, thiab lwm yam). Niaj hnub nimno macroeconomics uas nws kim heev kev siv ntawm differential thiab txawv sib npaug. Piv txwv li, nyob rau hauv macroeconomics yog siv thiaj li hu ua yooj yim tswj ntawm lub neoclassical kev tshawb xav ntawm nyiaj txiag txoj kev loj hlob. Txawv sib npaug kuj siv nyob rau hauv biology, chemistry, automation thiab lwm yam tshwj xeeb disciplines. Tus naj npawb qhia tau hais tias lub teeb ntawm cov nuj nqi, uas yog siv thaum xaiv cov kev ua pejxeem kev loj hlob. Qhov no kwv yog tiav los ntawm txoj kev tswj.

Yog li ntawd, tam sim no ntau kev tshawb xav. Ordinary differential kab zauv hu ua nonidentical piv ntawm cov kev kawm muaj nuj nqi Y nrog ib tug neeg sab nraud sib cav X, feem ntau ntawm cov neeg sab nraud nce mus nce los X thiab cov derivatives ntawm qhov tsis paub hais muaj nuj nqi ntawm ib tug txiav txim. Muaj ntau ntau hom ntawm differential sib npaug, ntau ntawm cov uas tom qab nyob rau hauv no tsab xov xwm.

Txawv sib npaug yog:

1) Pa kab zauv I-th thiaj, thiaj muaj kev nyob rau hauv lub squares. Cov no, nyob rau hauv lem, muab faib mus rau hauv: differential sib npaug nrog separable variables; Control nrog sib cais ntau yam; niaj hnub zoo li tswj; linear tswj; Pes tsawg differential sib npaug.

2) tswj ntawm ntau dua kev txiav txim.

3) Tawm Control II-th thiaj, uas yog homogeneous linear tswj II-th thiaj nrog rau qhov coefficients thiab inhomogeneous linear tswj nrog rau qhov coefficients.

Control kuj solved nyob rau hauv ob peb txoj kev, feem ntau ntawm uas - lub Cauchy teeb meem, rau txoj kev Euler thiab Bernoulli, thiab lwm tus neeg.

Nyob rau hauv muaj ntau yam teeb meem ntawm kev lag luam, kev kawm txog zauv, technology yog tsim nyog los xam ib yam naj npawb ntawm cov kev khiav dej num txuam nrog txhua lwm yam ib qhov nqi ntawm cov kev tswj. Tom qab ntawd peb tuaj mus rau cov kev pab ntawm lub cev ntawm differential sib npaug: ib tug txheej ntawm sib npaug, txhua tus uas muaj xws li ib tug neeg sab nraud nce mus nce los, cov kev ua ntawm no ywj siab thiab lawv derivatives.

Yog hais tias lub system yog linear nyob rau hauv lub tsis paub hais tias kev khiav dej num, nws yog hu ua ib tug linear system ntawm differential sib npaug. Qhov system ntawm differential sib npaug yuav hloov los ntawm ib tug maub los, qhov kev txiav txim uas yog sib npaug zos rau cov xov tooj ntawm sib npaug.

Conversion tswj system mus rau ib kab zauv nyob rau hauv tej rooj plaub tiav los ntawm kev siv cov tshem tawm txoj kev.

Nyob rau hauv tas li ntawd rau tag nrho cov saum toj no, muaj linear tshuab nrog rau qhov coefficients, uas muaj peev xwm muab tau yooj yim daws tau los ntawm Euler txoj kev.