Palena pau calculus o ka oihana o kekahi a me kekahi mau aiaiiuo

Palena pau calculus mea he lālā o ka makemakika Ka Ikepili, a huli aku i ka derivative, differentials a me kā lākou mau hana i loko o ke ao o ka hana.

Ka moolelo o ka

Palena pau calculus i waho me he kuokoa hoʻoponopono i loko o ka lua o ka hapalua o ka 17th kenekulia, mahalo i ka hana o Newton a me Leibniz, ka mea i ua kālaiʻia i ke kumu o ka ai ma ka i ka ho omaulia ana o differentials, a nana i ka pilina ma waena o hoʻohui 'a me ka differentiation. No ka hahau ana i hoʻomohala a me ka i ka ho omaulia ana o integrals, ma ia aha i ke kumu o ka makemakika Ka Ikepili. Keʻano o kēia mau calculi wehe i ka hou laekahi manawa i loko o ka makemakika honua, a kena ae la i ka muli o hou ka hoʻopaʻi 'ana ma ka' epekema. Nō hoʻi mai nae i ka manawa kūpono o ana makemakika ma ka sciences maoli a me ka hana 'enekinia,.

walaʻauʻana manaÿo

Palena pau calculus ua ma muli o ke kumu manaÿo o ka makemakika. Ka mea, e: he maoli helu, ka hoʻomauʻana a me ka palena o ke kuleana pili i. Ma hope o ka manawa, ka mea, ua lawe i ka laekahi nānā, mahalo i ka integral a me ka palena pau calculus.

Ke kaʻina hana o ka pili ana

Ho okumu ana o ka palena pau calculus ma ke ano o ka palapala noi, a laila, i ka 'epekema iaoia ana ma mua o ka muli o philosophical kumumanaʻo, a i hanaia e Nikolay Kuzansky. Kana hana ua manaoia e lilo i evolutionary kūpono 'ana mai i ka' epekema kahiko o ka hoʻoponoponoʻana. I loko nō o ka mea i ka poe akeakamai iho ua ole he mathematician, i kana makana i ka hooulu ana o ka makemakika 'epekema mea C. Brewer. Cusa, kekahi o ka mai mua mai o ka noonoo o ka makemakika like ka loa pololei 'epekema, makemakika ana i ka manawa i nīnau.

I ka wä kahiko mathematicians ao ana i ka pa alima, oiai ka poe akeakamai i manaoia like me ka hou ana infinity hoʻi i ka kiko'ī helu. Ma pili ana me keia Kuapo e hoohalike ai o ka pololei ma ka makemakika 'epekema. 'Epekema ka ike, ma kona manao, ua maheleia i loko o ka naauao a me ke akamai. Ka lua o ka mea oi pololei, e like me ke nä känaka 'epekema, mai ka mua haawi wale He kokekau wale hopena.

manaʻo

Ua hoʻokumu paʻa manaʻo, a me ka manaʻo o ka palena pau calculus pili i ka hana i loko o ka uuku kaiāulu o kekahi mau kumu. No keia mea, he mea pono ke hana i ka makemakika i hoʻomākaukauʻia e Launch haʻawina nona ka hana i loko o ka uuku kaiāulu o nā kumu i hoʻouka kekahi pili i ka hana o ka laina papa a me ka polynomial. Ma muli o kēia ho'ākāka 'ana o derivative a me ka palena pau.

Ke muli o ka manaʻo o ka derivative i kauoha ia e ka helu nui o ka pilikia o maoli sciences a me ka makemakika, a alakai ai i ka manao paa o ke kali aiee o ka iaʻano.

Kekahi o ka papa kuhikuhi hana i i haawiia mai e like me lakou i mea hoike, e hoʻomaka ana me ka papa kahiko kula, mea e hooholo i ka mämä holo o ke noi ana o kekahi wahi ma ka pololei o ka laina, a me ka hana ana o ka tangent laina a hiki i keia hālawa. Ka palena pau ua hoʻopili i keia, no ka mea, Ua hiki e He kokekau wale i ka hana i loko o ka uuku kaiāulu no kaʻoi o ka laina kuleana pili i.

Ke hoʻohālikelike a me ka manaʻo o ka derivative o ka hana o ka maoli ee iaaanu aey, ka wehewehena o differentials wale ae ma o ka hana ana o kekahi mau ano, ma ka like o ka ano o ka Euclidean pokole i kekahi.

derivative

E ka wahi e neʻe aku i loko o ke ala e hiki aku ana i ka y-axis, no ka manawa lawe mākou m, i ua ana, mai ka hoomaka ana mai o ka manawa. Kākau pili e like me ka neʻeʻana o hiki ma ka papa y me = f (x), a ua pili i kēlā me kēia manawa wahi m i kahi kūlike o displaceable wahi. Kēia papa kahea i mechanics e lawe kānāwai o ka noi. O ka papa kuhikuhi ano o ke noi, pakahi aku la ia haoʻa, o ka instantaneous māmā holo. A i ka wahi ua hoʻoneʻe ma ka y-axis e like me ke kānāwai o mechanics, ka kaulele manawa wahi mea loaʻa iā ia kekahi i kahi kūlike o m f (x). I ka manawa wahi m + Δh, kahi Δh ho i ka xi o ka manawa, ka mea e kordinaty f (x + Δh). Pela i hana haʻilula Δy = f (x + Δh) - f (x), a ua kapaʻia he kuleana pili i xi. He He wahi no ke ala kaahele aku la oia iloko o ka manawa mai m i ka m + Δh.

I e pili ana me ka hanana o ka māmā holo i manawa derivative ua lawelawe. Ke derivative o kekahi kuleana pili i ma ka paa wahi kapa i ka palena (holoholo ka mea i koe). Ua hiki e haawiia i kekahi mau huapalapala:

. f '(m), y me', Y, df / dx, dy / dx, Df (m).

Ke kaʻina hana o ka helu ana i ka derivative o ke kahea differentiation.

Palena pau calculus o ka oihana o kekahi mau aiaiiuo

Keia hana ua hoopili papa ao, kekahi mau aiaiiuo ka wā helu ana. Wā, he mau aiaiiuo xa me y, me ka hapa derivative me ka pili ana i ka m ma ka welau A ua kapaia ka derivative o keia hana ma ka m me ka paa y me.

Hiki e hōʻikeʻia hoʻi ke kēia mau hōʻailona:

. f '(m) (m, y me), Liliʻu' (m), ∂u / ∂x a me ka ∂f (m, y me) '/ ∂x.

koi 'ia ke kūlana mākaukau maoli

I mea e ana aʻo, a e hiki ke hoʻoponopono i diffury koi 'ia nā mākau i ka hoʻohui' a me ka differentiation. E hana ia maʻalahi e maopopo i ka palena pau nā helu kaulike, pono e hoomaopopo kumuhana derivative a indefinite integral. No hoi, aole e hana ino i ka aʻo, e nana i ka derivative o ka implicit kuleana pili i. O ke kumu ho i ka mea i loko o ke kaʻina hana o ka hoʻonaʻauao, e pinepine hoʻohana integrals a me differentiation.

Ano o ka palena pau nā helu kaulike

ʻaneʻane a pau ka hooponopono ana hana pili i ka mua-mea palena pau nā helu kaulike, eia 3 hoailona ia mea o nā helu kaulike: homogeneous, me ka separable DEBFULLNAME, laina inhomogeneous.

Aia mau no hoi oi pohihihi keia? Ueo nā helu kaulike me ka huina differentials, Bernoulli ka helu kaulike, a me na mea e ae.

paʻa pāʻoihana

E hoʻomaka, mākou e hoomanao mea algebraic helu kaulike o ke kula papa. Ka mea, aia no iloko olaila na aiaiiuo a me nā helu. I mea e hoʻoponopono i kaʻike mau helu kaulike e loaʻa nui o ka helu e panai ai i ke koho 'ia kulana. Nō kāu, i kēia mau nā helu kaulike i kekahi kumu, a no ka hōʻoia e panai wale nō i kēia nui i wahi i ike ole.

Ka palena pau helu kaulike mea like me keia. I mau, he helu kaulike o ka mua o ka papa maupaʻa:

• Kuokoa ee iaaanu aey.
• A derivative o ke kuleana pili i mua.
• Launch a e kaukaʻi ee iaaanu aey.

Ma kekahi mau hihia, aole e e ole i kekahi mea ike ole ia, m a me y me, akā, ia mea,ʻaʻole like nui me ka mea i pono, e i ka derivative mua, me ka ole kiekie kauoha nā mea loaʻa i ka pāʻoihana a me ka palena pau calculus, he oiaio ia mau mea.

Wehewehe i ka palena pau helu kaulike - ka mea, 'o ia hoʻi, e loaʻa i ka' ia paha o nā hana i kūpono ai ka manaʻo. Ia e puhi ia o ka oihana ua pinepine kapaia ka mau pāʻoihana ana.

integral calculus

Integral calculus o kekahi o na pauku o makemakika Ka Ikepili, a huli aku i ka manaʻo o integral, ka waiwai a me ka hakakā o kona i ka ho omaulia.

Pinepine i ka i ka ho omaulia ana o ka integral ia lŘlŘ ka wā helu ana i ka wahi o ka curvilinear shape. Ma keia o ia hoʻi, he kali āpana, i a me ka hoʻoholo ma mua wahi no ka kākauʻia iieeaii kinona me ka gradual mahuahua i loko o kona lima, a me kaʻaoʻaoʻikepili i ke i emi ma mua o kekahi mua i hoakaka ia ākeʻakeʻa kumu uuku cia.

Ke kiʻi i ka manaʻo i loko o ka i ka ho omaulia ana o ka wahi o kekahi geometric kinona ka helu ana i ka wahi o ka rectangle, alaila, he mea hōʻike i kona wahi, ua like no ka huina hoonui o ka lōʻihi ma ka laula. I ka wa e hele mai i ka anahonua, a laila, na? Ieoaeunoaa iauaeoia a pau i i ka hoʻohana 'ana i ka lula a me ka panana, a laila, i ka lākiō o ka lōʻihi i ka laula o ka naauao nui. I ka helu ana i ka wahi o ka triangle akau hiki ke nānā 'ia inā' oe i kekahi la ae, triangle, ua hanaʻia he rectangle. Ma o ka wahi o ka parallelogram i mau hōʻailona i loko o ka like akā iki hou huikau iaoia, i loko o ka rectangle, a me ka triangle. Ma o ka wahi o ka iieeaii ua noʻonoʻoʻia e triangle mauna komo i loko o laila.

Ma ka hoomaopopo ana i ke aloha o ākeʻakeʻa kumu, keia iaoia 'aʻole e pono ke hālawa. Inā mākou e uhai ia i loko o kanaka mika pāhoʻonui lua, ka mea e noho unfilled wahi. Ma keia hihia, e ho'āʻo i ka hoʻohana mau kapa komo, a me rectangles ma luna a ma lalo, e like me ka hopena o ia mau loaʻa i ka pakuhi o ka papa, a 'aʻole helu'. Nuiʻaneʻi mea he ala e wāwahi i kēia mau rectangles. Nō hoʻi, inā mākou e lawe i kaʻoluʻolu o ka nui a me ka oi hoemi, i ka wahi o ka luna a me lalo e converge ma luna o kekahi o kekahi waiwai.

Ka mea, e hoʻi i ka papa hana no ka hookaawale ana i loko o rectangles. Aia i mau Popular ano.

Riemann Ua formalized ka wehewehena o ka integral, hana e Leibniz a me Newton, e like me ka wahi o ka subgraph. Ma keia hihia, ua noʻonoʻo i kekahi kii iloko olaila o kekahi mau helu o vertical rectangles loaa mai ma ka mahele ana i ka wā mawaena. I ka uhaʻiʻana i ka emi ma laila mea he kali i ka i, ua kapaia ka hoemi wahi o ia o ka huahelu keia kali ka Riemann integral o ka papa ma ka hoakaka wā mawaena.

A lua o ka hana mea e kapili i ka Lebesgue integral, iloko olaila i loko o ka mea ia i loko o ka wahi o ka hookaawale ana i koho wahi ma luna o kekahi hapa o ka integrand, a i hoʻouluulu laila ka integral huina o na loina i loaa i loko o kēia mau wahi, maʻanuʻu no i puunaue i ka huahelu o cia, a laila, summed me ka AYEIE ana inverse nā kiʻi o kēia mau integrals.

kēia kōkua iā ia,

Kekahi o ka papa kuhikuhiE pomaikai no ka hoʻopaʻa 'ana i ka palena pau a me ka integral calculus Fikhtengol'ts kākau ihola - "o ka palena pau a me ka integral calculus." Kona puke mea he kumu paahana no ka hoʻopaʻa 'ana i makemakika Ka Ikepili, i ku e he nui a paʻi a me nā unuhi i loko o nā' ōlelo a pau. Created no nā haumāna, a no ka lōʻihi manawa hoʻohana ma o ka likeʻole ma o ka hoʻonaʻauao hui me kekahi o na kumu nui pomaikai o ka mahele. Ua haawiʻimi naʻauao 'ike a me ka mea hiki mākau. First paʻi i ka 1948.

Algorithm noiʻi kuleana pili i

E makaikai i na ki ina hana like o ka palena pau calculus hana, e pono e hahai ua ua haawiia algorithm:

1. E huli i ke kikowaena o ke kuleana pili i.
2. E huli i nā aʻa o ka haawi mai ai helu kaulike.
3. E huli i nā ihola. E hana i kēia, ua ho omaulia i ka derivative, a me ka wahi kahi i mea like me ka 'Aʻohe.
4. Mākou e panai i ka waiwai i loaa i loko o Eq.

ʻano likeʻole o ka palena pau nā helu kaulike

Hooponopono ana o ka mea mua o ka papa (i ole ia, palena pau calculus o kekahi ee iaaanu aey) a me ko lakou mau hoailona ia mea:

• Me ka separable aiaiiuo helu kaulike: f (y me) dy = g. (M) dx.
• Na simplest helu kaulike a me ka palena pau calculus hana o kekahi ee iaaanu aey, me ka haʻilula: y me '= f (x).
• I ka laina mua-mea nonuniform e hooponopono: y me '+ P (x) y me = Q (m).
• Bernoulli palena pau helu kaulike: y me '+ P (x) y me = Q (m) y me kekahi.
• Helu kaulike huina differentials me: P (x, y me) dx + Q (m, y me) dy = 0.

Ka palena pau nā helu kaulike o ka lua o ka papa, a me ko lakou ano:

• Homogeneous laina lua o ka papa palena pau helu kaulike me ka ikaika ^{coefficients: y me N + py '+ qy} = 0 p, Q no ka R.
• Inhomogeneous laina lua o ka papa palena pau helu kaulike me ka ikaika coefficients ^{waiwai: y me N + py '+ qy} = f (x).
• Homogeneous laina palena pau ^{helu kaulike: y me N + pa (m)} y me '+ Q (m) y me = 0, a me inhomogeneous lua o ka papa ^{helu kaulike: y me N + pa (m)} y me' + Q (m) y me = f (x).

Palena pau nā helu kaulike a kiekie ae kauoha mai a me ko lakou mau hoailona ia mea:

• Ka palena pau helu kaulike, hiki ka ho'ēmiʻana o ka ^{mea: F (x, y me (k} ), y me (k + ^{1), .., y me (N)} = 0.
• A laina helu kaulike o kiekie mea ^{_{homogeneous: y me (N) + f (}} n- ₁₎ y me ^(N-1) + ... + [illegible] ₁ y me '+ [illegible] ₀ y me = 0, a me ^{_{inhomogeneous: y me (N) + f (}} N _-1) y me ^(n-1) + ... + [illegible] ₁ y me '+ [illegible] ₀ y me = f (x).

Kuʻina o ka hoʻoponopono i ka pilikia a me ka palena pau helu kaulike

Me ke kōkua o kākou e hooponopono i nā mākau 'ole wale makemakika a me physical pilikia, akā, i ka likeʻole pilikia o kālaimeaola,? Aneia iainiiaaiea, sociology a me na mea e ae. I loko nō o ka laulāʻano o nā kumuhana apau loa, e hahai i ka hookahi kūpili kaʻina no ka hoʻoponopono i kēia mau pilikia.

1. Unuhi aku la ia i hoʻoholo. Kekahi o ka loa pilikia kahua o ka hoʻonaʻauao, a pono i kā mākou pololei, no ka mea, i kekahi hewa, e alakai i ka pono hewa hualoaʻa. He mea pono e lawe i ka mooolelo a pau o nā kumumea ka heluna i ke kaʻina hana a me ka hooholo loiloi mua ana. It E e ma muli no hoi ma kūʻiʻo a me Logical hopena.
2. No ka hoʻoponopono nā helu kaulike. Kēia kaʻina E hiki i ka wahi mua, no ka mea, pono wale ikaika manaʻo o ka makemakika ho.
3. Ka Ikepili a me ka loiloi 'ana i nā hualoaʻa. Loko pāʻoihana E e auhau no ka mea hoʻonoho o ka mea hiki a me kaʻimi naʻauao waiwai o ka hopena.

An laʻana o ka pono o ka palena pau nā helu kaulike ma ka lapaau

E ho ohana i ke keʻena mana i loko o ke kula o ka lapaau ua loaʻa i loko o ka hana o ka epidemiological makemakika kükohu. Mākou e mai poina i ka mea i loaʻa kēia mau nā helu kaulike ma ka kālaimeaola a me ka kemika, a e kokoke ana i ka oihana lapaau, no ka mea, Radio kūlana nui i ka hoʻopaʻa 'ana i kekahi mau liluwelo populations a Nine Inch keʻano o ka hanaʻana i loko o ke kanaka kino.

Ma keia hana, ke ahulau laha o ka maʻiʻaʻai hiki ke hana i loko o ka noho kaʻawaleʻana kaiaulu. Nā poʻe e noho ana i maheleia i ekolu hoailona ia mea:

• Iho mailoko o, ka helu o ka m (Halau), a oia no kanaka, infectious nā moku halihali mokulele, kela mea keia mea o ka i mea infectious (incubation au mea pōkole).
• Ka lua oʻano kikowaena susceptible kanaka y me (k), hiki ke iho mailoko o ka hui 'ana me mailoko o.
• Ke kolu oʻano kikowaena refractory kanaka Z (k), i nā'ōnaehana paleʻea a lilo no i ka maʻi.

Ka helu o nā kanaka mau, ka malama ana i hanau ai, ma kona ano maoli i make a me ka poʻe Polenekia uaʻaʻole noʻonoʻo pono. Ma ka Kora naʻEsau, e ia mau hypotheses.

Pakeneka maʻi i kekahi manawa wahi mea like i ka m (T) y me (Halau) (ma muli mea mahuʻi ma luna o ka pähola 'ana o ka helu ana o na hihia i like me ka helu ana o Huina ma waena o nā mea maʻi, a pane maʻalahi lala, a ma mua kokekau ka hapaʻauhau i ka m (T) y me (k)), i loko o no ia mea, ua mahuahua ka helu o ka hihia, a me ka helu o susceptible emi iho i ka uku, he pōpilikia ma ka haʻilula koʻi (Halau) y me (Halau) (i> 0).

Helu o ka ole-responders holoholona i make ai loaa e hoʻonele, mahuahua i ka uku a ka hapaʻauhau i ka helu o ka hoopii, bx (k) (b> 0).

E like me ka hopena, e hiki ke kau i ka'ōnaehana o nā helu kaulike a me nā mea a pau na nā hoailona ekolu ma ka muli o kona manaʻo iho.

Eia kekahi laʻana hoʻohana? Aneia iainiiaaiea

Palena pau calculus ua pinepine hoʻohana 'ia i loko o aneiai Ka Ikepili. O ka papa kuhikuhi hana i loko o ka waiwai Ka Ikepili ua manaoia e ia i ke ao ana o na aiee o ka hoʻokele waiwai, a i kākau i loko o ka palapala o ke kuleana pili i. Ua Ua hoʻohana 'ia i loko o ka hoʻoponopono pilikia e like me loli ma ka loaa auhau, piʻi pū koke hope, komo uku, loli i loaʻa ai ka wā hoʻololi i ka waiwai o ka huina hoonui, ma ka like ana hiki auou caiaiai ia e hoʻomaha aaiuo me ka hou lako a pan. E hoʻoponopono i ia pilikia, ka mea, ua koi 'ia e kükulu i kekahi palapala hana o ka hoʻopā ai DEBFULLNAME, a, ma hope o ka? Anoee ma ka palena pau calculus.

ia mea pinepine pono, e imi i ka loa e pono ai ke hana i loko o ka waiwai poepoe: i kā mākou productivity, ka mea kiekie loa makahiki, uuku kāki, a no laila, ma luna o. Kēlā me ia ke keʻena nei i ka hana ana o kekahi a oi manaʻo hoʻopiʻi kū'ē. No ka laʻana, ka? Iecaianoaaiiie hiki ke noʻonoʻo me ka hana ana o ka hana a me ka kulanakauhale alii. Ma keia pili ana, loaa ia makou he kupono cia hiki ke hoemi i loaa i ka i kā mākou 'ole palena iki o ka hana ana o kekahi a oi aiaiiuo.

Na pilikia e ho okumu i ka papa o ka extremal pilikia i loko o ka waiwai kula, no ka mea e pono ai palena pau calculus. I ka wā o ka aneiai anakahi ua koi 'ia e kń a hoʻonui loa like me ka hana ana i nā mea kiko'î, ke xi hiʻohiʻona i kā mākou wahi hana i nā manaʻo hoʻopiʻi kū'ē, e mālama i ka' Aʻohe ina ka xi o ka manaʻo hoʻopiʻi kū'ē mālama i ka 'Aʻohe. I ole ia, i ka wa ia i heluia, e mālama ai i ka kekahi maikaʻi paha io waiwai, me ka hoakaka wahi mea i pono, no ka mea, ma ka hoʻoulu 'ole ka hōʻemiʻana i ka manaʻo hoʻopiʻi kū'ē hiki ke hoʻololi e kaukaʻi cia i loko o ka makemake ka ao ao. I ka palena pau calculus terminology, keia makemake aha i ke koi 'ia aku ana no kā mākou hana mea he' Aʻohe waiwai o kona derivative.

Ka pōʻaiawaiwai mea i uncommon pilikia o loaa ka extremum o ka hana ana o kekahi mau DEBFULLNAME, no ka mea, aneiai nā hoailona, ua i mai o na mea he nui aʻe. Oia nīnūnē i maopopo loa i loko o ke kumumanaʻo o ka mana o kekahi mau DEBFULLNAME, i ke ano o ka helu ana i ka palena pau. Ua pilikia ka lolouila ole wale maximized a minimized hana, akā, i hoʻokau '. Kēia mau nīnau hai aku i ka makemakika iaaiey, a ua Wehewehe i nā hāʻina me i ke kōkua o ka pela 'epekema i ka nānā' ana ma luna o kēia lālā o ka 'epekema ka mea.

Mawaena o na ki ina hana like o ka palena pau calculus ia i loko o ka hoʻokele waiwai, he pauku nui o ka hope loa hoao. Ma ka waiwai poepoe, i ka manawa pili ia i ka lākou o ki ina hana like o ka noiʻi a ee iaaanu aey hana a me Nā hualoaʻa ma ka wā e hoʻololi i ka buke o ke hanaia, hokii, ma muli o ka Ikepili o ko lākou palena loina. Ke kaupalenaʻana PAaIEN noonoo derivative paha ka hapa 'nā mea loaʻa a me kekahi mau aiaiiuo.

Palena pau calculus o kekahi mau aiaiiuo - nui i kumuhana o ka makemakika Ka Ikepili. No ka piha ao, oe ke hana i kekahiʻano o ke ao kōkua iā ia, no ka mea kiekie oia ka hoʻonaʻauao kulanui. Kekahi o ka hana kaulana loa Fikhtengol'ts - "o ka palena pau a me ka integral calculus." Pehea ka nui o ka inoa no ke kākoʻo pāʻoihana o ka palena pau nā helu kaulike o ka huakaʻi nā e i ke akamai pū nō hoʻi, e hana me ka integrals. A hiki aku ka mea, he palena pau calculus o ka oihana o kekahi iaaanu, i ka hooholo ana i hiki. Oiai, he mea pono e kaulana, ka mea, penei ka ia kumu rula. I mea, e noiʻi ana i ka hana o ka palena pau calculus, e hahai i ka ua na algorithm, a ua haawiia mai i loko o ke kula kiʻekiʻe, a me wale i ka iki huikau me ka hoike o ka hou aiaiiuo.