Ahlobene amanani: iindlela zokubala kunye nemizekelo

Mhlawumbi ingqikelelo ithe liqhelekile sonke ukususela kwisikolo samabanga aphakamileyo. Ngokuqhelekileyo abafundi abafumana ubunzima bokuqonda ukuba oku ngokungathandabuzekiyo into ebaluleke kakhulu. Oku ngenkuthalo kusetyenziswa kwiindawo ezahlukeneyo ubomi babantu, yaye abaninzi zobunjineli zisekelwe ngqo kwi izibalo afunyenwe ithe. Kodwa ngaphambi kokuqhubeka ukuba uhlahlelo yintoni na yemvelaphi amanani njengoko ukubala yaye apho baya kuza imidlalo, irhubhululo kancinci ibe imbali.

indaba

Ingcamango ithe, nto leyo isisiseko uhlalutyo zezibalo, ivulekileyo (ngakumbi ukuba bathi 'yasungulwa "kuba, njengokuba enjalo, ayikho kwindalo) Isaakom Nyutonom, sonke thina siyazi ukususela kokufunyanwa umthetho womxhuzulane. Yaba nguye lowo kuqala wasebenzisa olu lwazi physics nohlobo olubophelelayo isantya yokunyusa imizimba. Yaye izazinzulu ezininzi ndibulele Newton le fyabo esihle, kuba enyanisweni wenza isiseko umehluko kunye calculus ebalulekileyo, isiseko senyaniso yentsimi yonke zezibalo ngokuba "ukuxhomekeka kolungiso". Nokuba ngexesha ibhaso le-Nobel, mhlawumbi Newton ndakuzuza izihlandlo ezimbalwa.

Hayi ngaphandle kwezinye neengqondo ezinkulu. Ukongezelela Newton kuphuhliso asebenza buchopho esukela nengxam ezifana ingca- zezibalo njengoko Leonhard Euler, आयडेंटीफिकेशन iSazisi kunye Louis Gotfrid Leybnits. Kuyinto ngenxa kubo sinazo imfundiso calculus mahluko kwifomu apho ikhona unanamhla. Phela, lo Leibniz wafumanisa intsingiselo zejometri yalo ithe, leyo nto ngaphezu kwithambeka kodwa azikweli phezulu ukuya igrafu msebenzi.

Yintoni yemvelaphi amanani? Bit phinda oko kwenzeka esikolweni.

Yintoni yemvelaphi?

Cacisa le mbono ngeendlela ezininzi ezahlukeneyo. Incazelo elula: yezabelo - yiyo isantya umsebenzi tshintsho. Bonisa igrafu nawuphi na umsebenzi y ye x. Ukuba ayithanga tye, nto inazo amagophe kule grafu, amathuba yongeniselo nokuncipha. Ukuba uthatha nawuphi na lokuphumla omncane le shedyuli, kuya kuba icandelo umgca othe ngqo. Ngoko ke, umlinganiselo ubungakanani icandelo omncane we y ukuya ubungakanani x ukuququzelela, kwaye uya kuba yemvelaphi umsebenzi kwindawo elinikiweyo. Ukuba siqwalasela umsebenzi uphela, kunokuba kwindawo ethile, ukuba afumane umsebenzi ithe, okt uxhomekeke ethile kwi X y.

Ukongeza, ngaphandle intsingiselo ebonakalayo kwezi yemvelaphi njengomsebenzi yereyithi tshintsho, kukho kwakhona ngengqiqo yemigca. Kuyo, thina ngoku ukuxoxa.

Intsingiselo lwezibalo

amanani ahlobene ngokwabo inani elithile ukuba akukho ukuliqonda abaqhubeki nayiphi na intsingiselo. Kubonakala ukuba ithe leyo ibonisa nje ukuba izinga lokukhula okanye ukunciphisa umsebenzi, kwaye kwithambeka kodwa azikweli phezulu ukuya igrafu umsebenzi ngelo xesha. definition akucaci ngokupheleleyo. Makhe sihlolisise oko ngokweenkcukacha. Masithi kufuneka igrafu komsebenzi (ukuba inzala curve). Kuye inani olungenasiphelo lamanqaku, kodwa kukho iindawo apho kuphela ingongoma oyedwa ubuninzi okanye ubuncinane. Ngokusebenzisa nayiphi na indawo enjalo, ungenza ukrwele umgca ngqo, eza aa Incopho na igrafu umsebenzi ngelo xesha. Le line iya kubizwa ngokuba ilayini ezibambanayo kodwa azikweli. Ukuba sithe bayizisa kwisiphambuka se- esqwini inkabi. Ngoko ndizuze phakathi ilayini ezibambanayo kodwa azikweli kunye esqwini inkabi kunye engile iya kumiselwa ithe. Ngokucace kakhulu, kodwa azikweli phezulu le engela iya kulingana kuyo.

Makhe sithethe kancinci malunga iimeko ezithile nezakhi Makhe sihlolisise amanani.

iimeko ezizodwa

Njengokuba sele sitshilo, avela amanani - ixabiso livela ngexesha elithile. Apha, umzekelo, ukuthatha umsebenzi y = x ^2. Le livela x - manani, kodwa jikelele - umsebenzi lingana 2 * x. Ukuba kufuneka ukubala uvumelane, umzekelo, kwindawo x ₀ = 1, sifumana y '(1) = 2 1 = 2. Yinto elula kakhulu. Ityala umdla lo yemvelaphi inani leqela. Ukuya inkcazelo eneenkcukacha malunga nokuthe inani leqela, angeke. Kwanele ukuba athi ukuba eli nani enoku iyunithi ebizwa ngokuba wentelekelelo - inani ogama isikwere ilingana -1. Ukuze kubalwe le ithe kunokwenzeka kuphela phantsi kwale miqathango ilandelayo:

1) Kufuneka kubekho yokuqala umyalelo yezabelo isixa sazo iinxalenye lokwenene elisetyenziswa ukulinganisela y kunye X.

2) imiqathango Cauchy-Riemann ezinxulumene ukulingana buso ochazwe kumhlathi wokuqala.

Elinye icala umdla, nangona njengokuba nzima kowangaphambili, i yemvelaphi inani elithabathayo. Enyanisweni, naziphi amanani akhabayo angamelwa okuhle, iphindwe -1. Kaloku, lo yemvelaphi kwaye umsebenzi rhoqo elingana ne-njalo liphindaphindwe yemvelaphi lo msebenzi.

Kuya kuba umdla ukufunda malunga nendima avela kubomi babo bemihla ngemihla, yaye oku ngoku nize nixoxe ngawo.

isicelo

Mhlawumbi ngamnye kuthi ubuncinane kanye ebomini ukubamba ngokwam ndicinga ukuba kwimathematika kungenakwenzeka ukuba abe luncedo kuye. Yaye into enzima enjalo njengoko ithe mhlawumbi akukho ukusetyenziswa. Enyanisweni, izibalo - inzululwazi esisiseko, yaye zonke iziqhamo zayo uvela ikakhulu physics, chemistry, ngeenkwenkwezi kunye noqoqosho. Uvumelane aphawula ukuqala ukuxhomekeka kolungiso, owasinika eli thuba ukwenza izigqibo ukusuka iigrafu imisebenzi, yaye siye safunda ukutolika imithetho yendalo kunye bababuvisele inzuzo yabo ngenxa kuyo.

isiphelo

Kakade ke, asinguye wonk 'umntu kunokuba luncedo ukuba yemvelaphi ebomini. Kodwa nezibalo iphuhlisa logic eziya kufuneka. Kungekho nto kuba zemathematika kuthiwa ukumkanikazi Sciences: oko kuba nolwazi olusisiseko kwezinye iinkalo zolwazi.