Umehluko zibalo - ngokuthe gabalala and Scope

Ukufunda ngeziganeko zendalo, iingxaki imisebenzi eyahlukeneyo nakwezoqoqosho, ibhayoloji, isayensi, ubunjineli, akusoloko kusenzeka ukuba ukuseka nangoko ikhonkco ngqo phakathi ngabanye imilinganiselo ezichaza inkqubo ethile ngamabonandenzile. Ngokubanzi, umntu ukufumanisa ubudlelwane phakathi kwezi amaxabiso (imisebenzi) kunye izinga utshintsho ngokuphathelele omnye (ezizimeleyo) bume. Oku kuphakamisa zibalo apho imisebenzi ezingaziwayo baphantsi umqondiso ithe - i'quadratic umahluko. Kolu phando lwabo kokuchitha ixesha elininzi, oluninzi izazinzulu abadumileyo: Newton, Bernoulli, Laplace kunye nabanye. Ukusetyenziswa umehluko zibalo zilangazelelwa: imifuziselo nemiba yezoqoqosho, ukubonisa kuphela umahluko abaxhomekeke kwexesha, kodwa ulwalamano lwabo kwexesha, xa iingxaki ngemithamo kunye Uqoqosho lwesizwe; sebenzisa ukuba ukuchaza andise amaza nobushushu, ngezimanga ezahlukeneyo yendaleko ukuba kwenzeka eziphilayo nezingaphiliyo indalo.

Ngoncedo amaza ukudlulisa ulwazi kumgama (umabonakude, ngomnxeba, unomathotholo, njl njl). Uqoqosho Modern siyisebenzise kakhulu umehluko kunye umahluko zibalo. Ngokomzekelo, xa Uqoqosho isetyenziswa-ekuthiwa ulawulo olusisiseko theory neoclassical zokukhula koqoqosho. umehluko zibalo nazo kusetyenziswa eziphilayo, chemistry, isilawuli esizisebenzelayo kunye nezinye iinkalo ezikhethekileyo. Lo mzobo ubonisa igrafu umsebenzi, nto leyo iya kusetyenziswa xa kunikwa ingqalelo ukukhula yokwanda kwabantu. Le into kuphunyezwa iindlela zolawulo.

Ngoko ke, theory ngoku ngakumbi. EziQhelekileyo zahlula equation ekuthiwa ratio nonidentical phakathi umsebenzi Y efunekayo omnye ezizimeleyo ingxabano X, ukuba inkoliso X elitshintshayo ezizimeleyo yezabelo komsebenzi olungaziwayo lwe ngendlela ethile. Kukho iintlobo ezininzi umehluko zibalo, ngakumbi apho kamva kweli nqaku.

umehluko zibalo zezi:

1) equation eziQhelekileyo umyalelo I-th, zinxulunyaniswe kwiindawo zembutho. Ezi zicwangciso, ziya, yahlulwe: umehluko zibalo kunye variables separable; Ulawulo kunye nesebenzayo bahlukana; ulawulo olufanayo; ulawulo linear; umehluko zibalo obububo.

2) ukulawula kweliphezulu.

3) ukuze Linear Control-II th, ezo ulawulo yomgama yohlobo olunye ukuze-II th kunye okuza rhoqo kunye nolawulo inhomogeneous yomgama kunye okuza rhoqo.

Control kwakhona isonjululwe ngeendlela ezininzi, yeyona ixhaphakileyo apho - ingxaki Cauchy, iindlela Euler kunye Bernoulli, kunye nabanye.

Xa iingxaki ezininzi-Economics, iMathematics, iteknoloji kuyimfuneko ukubala inani elithile kwemisebenzi ezinxulumene namanye isixa esithile nganye yolawulo. Ngoko ke ubavelele kwenkqubo umehluko zibalo: iseti zibalo, nganye ebandakanya i-bume ezimeleyo, umsebenzi yalo ezizimeleyo kunye nezakhi zawo.

Ukuba inkqubo lwento kwi imisebenzi ezingaziwayo, ibizwa ngokuba inkqubo ngokulandelelanayo ye umehluko zibalo. inkqubo eqhelekileyo umehluko zibalo na kutshintshwa kuze kufakwe omnye umlawuli olunye, indlela apho lilingana nenani kwizibalo.

inkqubo yolawulo Conversion ukuya equation enye kwezinye iimeko kufezwa ngokusebenzisa indlela emzimbeni.

Ukongeza konke oku kungentla, kukho iinkqubo linear kunye okuza rhoqo, nto leyo kube lula isonjululwe indlela Euler kaThixo.