Differential Equations - General Information uye Makuriro

Kudzidza mananara zvakasikwa, nekugadzirisa mabasa akasiyana-siyana ari dzezvoupfumi, zvipenyu, wefizikisi, engineering, kwete nguva dzose zvinoita kuti pakarepo kumisa kwainge pakati nedzimwe tsika zvinorondedzera yakati shanduka kwacho. Kazhinji, munhu anogona kuona ukama pakati tsika idzi (Mabasa) ravo zvazvingava yokuchinja panyaya vamwe (akazvimirira) shanduka. izvi zvinomutsa equations umo zvisingazivikanwi mabasa vari pasi chiratidzo rinobva - a differential mukana wokuti vanhu vanga. Pakudzidza takapedza nguva yakawanda, chaizvo nomukurumbira masayendisiti: Newton, Bernoulli, Laplace nevamwe. Kushandiswa differential equations vari zvikuru: yokutevedzera zvoupfumi emuchina, kuratidza kwete chete pakufambira shanduka nguva, asi ukama hwavo nguva, muna zvinetso micro- uye macroeconomics; kuzvishandisa kutsanangura Mashoko remagetsi uye pokupisa, uye siyana shanduka mananara kuti kuitika pakurarama uye asiri mupenyu hunhu.

Achibatsirwa remagetsi mafungu wokushandura mashoko nechokure (terevhizheni, foni, redhiyo, etc.). Modern macroeconomics akakura kushandisa differential uye musiyano equations. Somuenzaniso, mune macroeconomics rinoshandiswa inonzi chikuru kudzora neoclassical dzidziso zvoupfumi kukura. Differential equations dziri kushandiswa zvipenyu, kemisitiri, kushandisa michina nezvimwe chaiwo anoranga. The mufananidzo chinoratidza girafu pamusoro basa, rinoshandiswa kana kufunga kuwedzera kwouwandu hwevanhu. chinhu ichi kunoitwa pachishandiswa kuzvidzora.

Saka, zvino zvakawanda dzidziso. Munhuwo differential mukana wokuti vanhu vanga rinonzi nonidentical reshiyo pakati aida basa Y mumwe akazvimiririra nharo X, kupfuura pamusoro akazvimirira shanduka X uye nomukaka zvausingazivi basa womumwe kurongeka. Kune mhando dzakawanda differential equations, zvakawanda zvacho gare gare munyaya ino.

Differential equations ndiwo:

1) kwakajairika mukana wokuti vanhu vanga I-fung murayiro, vari revatema napamatare. Ivavawo, akakamurwa: differential equations pamwe kupatsanurwa variables; Kuzvidzora pamwe vakaparadzana variables; hinifomu kuzvidzora; Linear kuzvidzora; Chaiyo differential equations.

2) kudzora yakakwirira kurongeka.

3) Linear Control II-fung kuti, izvo homogeneous Linear kuzvidzora II-fung kuitira pamwe kugara coefficients uye inhomogeneous Linear kuzvidzora pamwe kugara coefficients.

Kuzvidzora zvakare chakagadziriswa nenzira dzakawanda, vakawanda iyo - the Cauchy dambudziko, nzira Euler uye Bernoulli, uye vamwe.

In matambudziko akawanda dzezvoupfumi, masvomhu, unyanzvi hwokugadzira zvakakodzera kuverenga imwe nhamba mitambo chokuita nomumwe imwe mari kudzora. Zvadaro tinosvika kubatsira ezvinhu differential equations: chine equations, nerimwe zvinosanganisira yakazvimirira shanduka, mashandiro ichi akazvimirira uye dzavo nomukaka.

Kana hurongwa iri Linear ari isingazivikanwi kushanda, inonzi ine Linear hurongwa differential equations. Normal Tsika differential equations zvinogona chikatsiviwa chete controller, Unorudzi chiri zvakaenzana nokuwanda equations.

Kutendeuka kudzora mamiriro mumwe mukana wokuti vanhu vanga dzimwe nguva nokushandisa kubviswa nzira.

Kuwedzera kune vose pamusoro, pane Linear enyika pamwe kugara coefficients, izvo zvinogona nyore kugadziriswa Euler kuti nzira.