Umzekelo wemodeli yemathematika. Inkcazo, udidi kunye nezixhobo

Kwinqaku, enikezelwa ngqalelo, sinika imizekelo yemodeli yemathematika. Ukongezelela, siya kuqwalasela amanyathelo okudala imodeli kwaye sihlalutye ezinye iingxaki ezinxulumene neemodematika.

Omnye umbuzo esinawo imodeli yemathematika kwizoqoqosho, imizekelo, esiya kuyiqwalasela kamva. Sincoma ukuqala incoko yethu kwingcamango yolu "mzekelo", uhlaziye ngokufutshane ulwahlulo lwabo kwaye uqhubele phambili kwimicimbi yethu ephambili.

Umxholo othi "umzekelo"

Sivame ukuva igama elithi "imodeli". Yintoni na? Eli gama linenkcazelo eninzi, nango amathathu kuphela:

• Into ethile eyenzelwe ukufumana nokugcina ulwazi, ukubonakalisa ezinye iipropati okanye iimpawu, kunye nokunye okokuqala yile nto (into enje ingabonakaliswa ngeendlela ezahlukeneyo: ingqondo, inkcazo ngeendlela zempawu kunye njalo);
• Nangona phantsi komzekelo kuthetha ukubonakaliswa kweemeko ezithile, ezibalulekileyo okanye zolawulo;
• Imodeli ingaba ikopi eyancitshisiwe yento (ayidalwe ukufundisisa ngokubanzi kunye nokuhlalutya, kuba umzekelo ubonisa isakhiwo kunye nolwalamano).

Ngokusekelwe kuyo yonke into eyayishiwo ngaphambili, unokwenza isigqibo esincinci: umzekelo uvumela ukuba ufunde ngokubanzi iinkqubo eziyinkimbinkimbi okanye into.

Zonke iimodeli zingahlelwa ngohlobo lweempawu:

• Kwintsimi yokusetyenziswa (imfundo, uvavanyo, isayense kunye nobuchwepheshe, umdlalo, ukulingisa);
• Amandla (i-static and dynamic);
• Kwisebe yolwazi (umzimba, iikhemikhali, indawo, imbali, ezentlalo, ezoqoqosho, izibalo);
• Ngendlela yokubonisa (izinto kunye nolwazi).

Iimodeli zolwazi, ngokwazo, zihlulwe zibe ngumqondiso kunye nezivakalisi. Kwaye iimpawu ezibonakalayo zekhompyuter kunye non-computer. Ngoku ke masibuyele kwingqwalasela ecacileyo yemizekelo yemodeli yemathematika.

Imodeli yeMathematika

Njengoko kunzima ukuqikelela, imodeli yeemathematika ibonisa ezinye iimpawu zento okanye into esebenzayo usebenzisa iimpawu ezizodwa zemathematika. Imathematika iyadingeka ukubonisa imigaqo yehlabathi elijikelezayo ngolwimi oluthile.

Indlela yokwenza imathematika yazalwa ngokudala, amawaka eminyaka edluleyo, kunye nokufika kwesi senzululwazi. Nangona kunjalo, ukukhuthazwa kwendlela yokwenza imodeli kwakubakho ukuvela kwamakhompyutha (iikhomputha zekhompyutha).

Ngoku ma siqhubeke nokuhlelwa. Inokwenziwa kwakhona kwezinye iindawo. Ziyakwenziwa kwitafile ngezantsi.

Siphakamisa ukuyeka nokuphonononga uluhlu olutshanje ngokubanzi, kuba lubonisa iindlela eziqhelekileyo zokwenza imodeli kunye nenjongo yemodeli eyenziwe.

Iimodeli ezichazayo

Kule sahluko, siyancoma ukuba sihlale ngeenkcukacha ezininzi kwiimodeli ezichazayo zeemathematika. Ukuze yonke into icace, umzekelo uya kunikwa.

Okokuqala, le ntlobo ingabizwa ngokuba ichazayo. Oku kubangelwa ukuba sinokwenza izibalo kunye nezibikezelo, kodwa asikwazi ukuchaphazela umphumo wesiganeko nangayiphi na indlela.

Umzekelo ocacileyo wemodeli yeemathematika echazayo yinkqutyana yendlela yokuhamba kwendiza, isantya, umgama ukusuka kuMhlaba we-comet, owangena kwi-system ye-solar. Lo mzekelo uchaza, kuba zonke iziphumo ezifumanekayo zingasilumkisa nje nayiphi na ingozi. Ukuchaphazela umphumo wesiganeko, hayi, asikwazi. Nangona kunjalo, ngokusekelwe kwizibalo ezifunyenweyo, kunokwenzeka ukuthatha nawaphi na amanyathelo okusindisa ubomi emhlabeni.

Iimodeli zokulungisa

Ngoku siza kuthetha kancinci ngemodeli yezoqoqosho kunye neemathematika, imizekelo yezinto ezinokwenza izimo ezahlukeneyo. Kule meko, sithetha ngamanqaku anceda ukufumana impendulo efanelekileyo phantsi kweemeko ezithile. Zineempawu ezithile. Ukuze kucace kakhulu, cinga ngomzekelo ukusuka kwinqanaba legrarian.

Sinegranari, kodwa ingqolowa ilahleka ngokukhawuleza. Kule meko, kufuneka sikhethe ngokufanelekileyo ulawulo lwamaqondo okushisa kunye nokwandisa inkqubo yokugcina.

Ngaloo ndlela, sinokuchaza "imodeli yokulungiselela". Ngomqondo wemathematika, le yinkqubo yokulinganisa (zombini kunye kwaye ayikho), isisombululo esinceda ukufumana isisombululo esiphezulu kwiimeko ezithile zoqoqosho. Sihlolisise umzekelo wemodeli yeemathematika (ubuchule), kodwa ndingathanda ukudibanisa: olu hlobo luseklasini yeengxaki ezigqithiseleyo, zinceda ukuchaza ukusebenza komsebenzi wezoqoqosho.

Masiqaphele enye into engafaniyo: imodeli ingaba nomntu ohlukileyo (jonga itafile engezantsi).

Iimodeli ezininzi zokumisela

Ngoku sicebisa ukuba uthethe omncinane ngemodeli yeemathematika ye-multicriteria. Ngaphambi koko, sinike umzekelo wemodeli yeemathematika yokucwangcisa inkqubo nayiphi na imilinganiselo, kodwa kuthekani ukuba kukho ezininzi?

Umzekelo ocacileyo womsebenzi we-multicriteria yintlangano yolungileyo, eluncedo kwaye ngexesha elifanayo ukondla ngokomoya ngokweqela elikhulu labantu. Ngeemisebenzi ezinjalo zivame ukufumaneka emkhosini, kwizikolo ze-canteens, kwiinkampu zasehlotyeni, kwizibhedlele njalonjalo.

Ziziphi iinkqubo ezinikezelwa kulo msebenzi?

1. Ukutya kufuneka kube luncedo.
2. Iindleko zokutya mazingabi ncinane.

Njengoko ubona, ezi njongo azihambelani nonke. Ngoko, xa usombulula ingxaki, kuyimfuneko ukukhangela isisombululo esiphezulu, ibhalansi phakathi kweendlela ezimbini.

Iimodeli zeMidlalo

Ukuthetha ngemidlalo yokudlala, kuyimfuneko ukuqonda ingcamango "ye-theory game". Ngokucacileyo, le mizekelo ibonisa imodeli yemathematika yeengxabano zangempela. Kuphela kukufanelekile ukuqonda ukuba, ngokungafani nongquzulwano lwangempela, imodeli yemidlalo yemidlalo inemithetho ethile.

Ngoku kuya kunikwa ubuncinci beenkcukacha kwi-theory yemidlalo, eya kukukunceda uqonde ukuba imodeli yomdlalo. Kwaye ke, kumzekelo kubakho amahlangothi (ezimbini okanye ngaphezulu), ezidla ngokuba ngabadlali.

Zonke iimodeli zinempawu ezithile.

Imodeli yomdlalo ingaba ibini okanye ezininzi. Ukuba sinezifundo ezibini, ngoko-mbambano yimbini, ukuba ngaphezulu - ezininzi. Ungakwazi kwakhona ukubona umdlalo ochasayo, ubizwa ngokuba ngumdlalo we-zero-sum. Lo ngumzekelo apho inzuzo yomnye wabathathi-nxaxheba ilingana nokulahlekelwa kwesinye.

Iimodeli zokulinganisa

Kule candelo, siya kuqwalasela umzekelo wemimodeli yemathematika. Imizekelo yemisebenzi yile:

• Umzekelo wendlela yokuguqulwa kweenombolo zamancinci;
• Umzekelo wesindululo seamolekyu, njalo njalo.

Kule meko, sithetha ngamanqaku athile asondeleyo kwinkqubo ngokwenene. Ngokubanzi, balingisa naluphi na ukubonakaliswa kwendalo. Kwimeko yokuqala, ngokomzekelo, sinokufanisa ukuguqulwa kwenani leentuthane kwikoloni enye. Kule meko, umntu unokugcina isiganeko somntu ngamunye. Kule meko, inkcazo yemathematika ayifumaneki isetyenziswa, ngokuqhelekileyo kukho izimo ezibhaliweyo:

• Kwiintsuku ezintlanu ibhinqa ibeka amaqanda;
• Kwiintsuku ezingamashumi amabini intyana iyafa, njalo njalo.

Ngako oko, imodeli yokulinganisa isetyenziselwa ukuchaza inkqubo enkulu. Isiphetho seMathematika sisisombululo seenkcukacha zesafi efunyenweyo.

Izidingo

Kubalulekile ukwazi ukuba ezinye iimfuno zibekwe kuloluhlobo lwemodeli, phakathi kwazo zizo zidweliswe kwitheyibhile elingezantsi.

Amanqanaba omzekelo

Ingqikithi yemodeli yeemathematika kuyisiko ukuhlukanisa izigaba ezine.

1. Ukuqulunqwa kwemithetho edibanisa iindawo zomzekelo.
2. Uphando lweengxaki zeemathematika.
3. Ukucacisa ukungalingani kwezinto ezibonakalayo kunye neziphumo.
4. Uhlalutyo kunye nokuhlaziywa kwemodeli.

Imodeli yoqoqosho-yemathematika

Kule candelo siza kuxoxa ngokufutshane ngolu hlobo lwemodeli yezoqoqosho nezemathematika. Imizekelo yemisebenzi yile:

• Ukusekwa kwenkqubo yokuvelisa imveliso yezilwanyana, okuqinisekisa ukuba inzuzo enkulu yokuvelisa;
• Ukuphakamisa inzuzo yentlangano ngokubala inani elifanelekileyo letafile kunye nezihlalo kwifenitshala yefenitshala, njalo njalo.

Imodeli yezoqoqosho-yemathematika ibonisa ukukhishwa kwezoqoqosho, okubonakaliswe ngokwemigangatho nemimiselo.

Imodeli yemathematika yekhompyutheni

Imizekelo yemodeli yeemathematika yekhompyutheni yile:

• ImiSebenzi yama-hydraulic ngoncedo lweempawu zebhloko, imifanekiso, iitafile, njalo njalo;
• Iingxaki kwi-mechanics yeziqulatho, njalo njalo.

Imodeli yekhompyutheni ngumfanekiso wento okanye inkqubo, emele:

• Iifayile;
• Iimpawu zokuhamba;
• Imifanekiso;
• Imizobo, kunye njalo.

Ngexesha elifanayo, lo mzekelo ubonisa isakhiwo kunye nokusebenzisana kwenkqubo.

Ukwakhiwa kohlobo lwezoqoqosho-lwemathematika

Sithe satsho malunga nokuba imodeli yezoqoqosho-imathematika. Umzekelo wesisombululo senxaki iya kuqwalaselwa kwangoku. Kufuneka senze uhlalutyo lwenkqubo yokuvelisa ukuchonga inzuzo yenkcitho eyongeziweyo ekutshintsheni kwoluhlu.

Asiyi kuqwalasela ngokupheleleyo ingxaki, kodwa kuphela ukwakha imodeli yezoqoqosho-imathematika. Umlinganiselo wethu womsebenzi kukunyusa inzuzo. Emva koko umsebenzi unalo ifomu: A = p1 * x1 + p2 * x2 ..., efikelela phezulu. Kulo mzekelo, ip isunithi nganye, x iyinombolo yeeyunithi ezivelisiweyo. Ukongezelela, ngokusekelwe kumzekelo owakhelweyo, kubalulekile ukwenza izibalo kunye nesishwankathelo.

Umzekelo wokwakha imodeli elula yemathematika

Umsebenzi. Umlobi wabuyela ngokubamba:

• 8 iintlanzi - abemi baselwandle;
• I-20% yabalobi-abemi bezilwandle zasemazantsi;
• Ukusuka kumlambo wendawo, akukho ntlanzi enye.

Zingaphi iintlanzi ayithenga kwivenkile?

Ngaloo ndlela, umzekelo wokwakha imodeli yeemathematika yenkathazo enikwe ngolu hlobo lulandelayo. I-Denote inani elipheleleyo leentlanzi x. Ukulandela imeko, i-0.2x yinani lentlanzi ehlala kwiindawo ezisemzantsi. Ngoku sidibanisa lonke ulwazi olufumanekayo kwaye sifumane imodeli yemodeli yenkinga: x = 0.2x + 8. Sombulula i-equation kwaye ufumane impendulo kumbuzo oyintloko: uthenge iintlanzi ezili-10 kwivenkile.