Kushandiswa kweMuganho weBasa
Muganho ipfungwa huru mukuverenga inotsanangura maitiro ebasa sezvo kupinda kwaro kunosvika pakukosha kwakati. Mumasvomhu, muganho webasa une basa rakakosha mukunzwisisa kukura, kuenderera mberi, uye kushanduka kwebasa. Pfungwa yemuganho ndiyo hwaro hwezvinhu zvinobva muzvinhu uye zvinhu zvakakosha, mbiru mbiri huru dzekuverenga. Kupfuura basa rayo redzidziso, miganho inewo simba guru pakushandiswa kwakasiyana-siyana, kubva pafizikisi kusvika kuhupfumi. Muchinyorwa chino, tichaongorora mashandisirwo emiganho yebasa munzvimbo dzakasiyana dzesainzi.
Tsanangudzo yeMuganhu
Nekunzwisisa, muganho webasa \( f(x) \) sezvo \( x \) uchiswedera \( c \) ndiyo kukosha uko \( f(x) \) kunowanzo kusvika sezvo \( x \) uchiswedera pedyo ne \( c \). Chinyorwa chemuganho uyu ndeichi:
\[ \lim_{{x \to c}} f(x) = L \]
kureva kuti, sezvo \( x \) ichiswedera \( c \), ipapo \( f(x) \) ichiswedera \( L \). Tsananguro yepamutemo yemuganhu inoshandisa pfungwa ye epsilon-delta kusimbisa kururama kwekufungidzira.
Mashandisirwo muFizikisi
Kufamba uye Kumhanya
Mufizikisi, miganhu inokosha pakutsanangura kufamba. Kumhanya kwechinhu panguva imwe chete ndiko kunobva panzvimbo yacho maererano nenguva. Semuenzaniso, kana nzvimbo yechinhu \( s(t) \) iri basa renguva \(t \), saka kumhanya kwekukurumidza \(v(t) \) ndekwekuti:
\[ v(t) = \lim_{{\Delta t \to 0}} \frac{s(t + \Delta t) – s(t)}{\Delta t} \]
Muganho uyu unotsanangura derivative yebasa renzvimbo, zvinoreva kuti velocity ndiyo mhedzisiro inoganhurira yehuwandu hwekuchinja kwenzvimbo nenguva.
Mutemo wesimba rinokwevera pasi
Pfungwa yaNewton yegiravhiti inogonawo kutsanangurwa kuburikidza nemiganhu. Simba rinokwevera zvinhu pakati pezvinhu zviviri rinokanganiswa nedaro parinosvika zero. Izvi zvinowanzo ongororwa muzviitiko apo zvinhu zvinosvika pakati pehukuru kana giravhiti, uye miganhu inoshandiswa kunzwisisa simba rinoshanda padaro diki kana rakanyanyisa.
Zvikumbiro muEconomics
Mari Yekumucheto uye Mari Yekumucheto
Muzvehupfumi, mari shoma uye mari shoma inowanikwa kubva pamari yose inowanikwa pamwe nemari yose inowanikwa, zvichiteerana. Mari shoma (MC) imutengo wekuwedzera wekugadzira imwe yuniti imwe, inotsanangurwa nemasvomhu se:
\[ MC = \lim_{{\Delta q \to 0}} \frac{TC(q + \Delta q) – TC(q)}{\Delta q} \]
apo \( TC \) iri basa remutengo wese uye \( q \) iri nhamba yemayuniti anogadzirwa.
Mari inowanikwa zvishoma yakafanana nepfungwa iyi uye inokosha pakuongorora kuenzana kwekambani uko \(MR = MC\) inotaura mamiriro ekuwedzera purofiti.
Zvikumbiro muUinjiniya
Kuongorora Kudedera
Muinjiniya netekinoroji, miganhu inoshandiswa kuongorora vibration uye dynamic systems. Semuenzaniso, mhinduro yesystem kune chiratidzo chiri kusvika pa resonant frequency yayo inogona kufanotaurwa uchishandisa miganhu. Uchishandisa nzira yeFourier transform, maitiro esystem frequency anogona kuongororwa kuti anzwisise mhinduro yayo nekufamba kwenguva.
Kuvimbika Kwezvinhu Uye Kukuvadzwa
Miganhu inobatsirawo pakufanotaura kuvimbika uye kukundikana kwezvinhu. Matekiniki akadai semakanika ekupwanyika anoshandisa miganhu kunzwisisa maitiro ezvinhu padanho diki (microstructural) uye kufanotaura nzvimbo yekukundikana kwezvinhu zviri pasi pekumanikidzwa kana kumanikidzwa.
Mashandisirwo muMasvomhu
Dzidziso yeKukosha kwePakati
Intermediate Value Theorem ipfungwa yekushandiswa zvakananga kwepfungwa yemiganhu. Inotaura kuti kana \( f(x) \) iri continuous pane interval \([a, b]\) uye \( L \) iri chero nhamba yakakwana pakati pa \( f(a) \) uye \( f(b) \), saka pane c imwe chete mu \([a, b]\) zvekuti \( f(c) = L \). Iyi theorem inozivikanwa mu root-finding algorithms.
Zvinobva uye Zvimisikidzo
Muganho webasa ipfungwa inokosha mutsanangudzo dzemaderivatives ne integrals. Derivative muganho wekuchinja kwebasa nekukurumidza maererano ne variable yaro yakazvimirira. Integral, kune rumwe rutivi, muganho wenzvimbo yese iri pasi pe curve yebasa pamusoro penguva yakatarwa, iyo inokoshawo pakuverenga kwakasiyana-siyana kwenzvimbo, vhoriyamu, uye mamwe mashandisirwo mufizikisi.
Zvikumbiro muBiology
Kuwedzera Kwevagari
Mamodheru emasvomhu anotsanangura kukura kwevanhu anowanzo shandisa miganhu kunzwisisa maitiro evanhu mumamiriro ezvinhu akaoma. Semuenzaniso, mumuenzaniso weMalthusian, huwandu hwevanhu hunokura zvakanyanya, uye miganhu inoshandiswa kuona maitiro evanhu kwenguva refu.
Maitiro eEnzymatic
Mu biochemistry, maitiro e enzyme anowanzo ongororwa uchishandisa Michaelis-Menten model. Muyero we reaction \(v\) sebasa re substrate concentration \(S\) unogona kusvika pamuganho mukuru sezvo huwandu hwe substrate huchiwedzera. Muganho uyu unobatsira kunzwisisa kushanda zvakanaka kwema enzymes.
Mashandisirwo muMakomputa neInformatics
Kuongorora Algorithm
Musainzi yemakombiyuta, miganhu inoshandiswa kuongorora kuomarara kwealgorithm. Zvinyorwa zvisina symptotic zvakaita seBig O, Omega, naTheta zvinotsanangura mashandiro ealgorithm mumiganhu yakanakisisa, yakaipa, uye yepakati. Miganho inopa hwaro hwemasvomhu hwekuverenga nekuenzanisa kushanda kwealgorithm pamusoro pehuwandu hukuru hwedata.
Kudzidza Kwemichina
Maalgorithms ekudzidza kwemuchina, kunyanya ayo ane chekuita nekuvandudzwa kwegradient, anoshandisa pfungwa yemiganhu kuti agadzirise mabasa ekurasikirwa. Kugadziriswa kwemaparamita kunoitwa mumatanho madiki kuti kusvike padanho repasi rose kana remunharaunda, uye maitiro aya ekudzokorora anoenderana nemiganhu yematanho madiki anotevedzana.
Mhedziso
Kubva pane zvataurwa pamusoro apa, zviri pachena kuti miganhu yebasa ine basa rakakosha muzvidzidzo zvakasiyana-siyana zvesainzi. Kuinzwisisa hakusi chete kwakakosha mudzidziso yemasvomhu asiwo kune mashandisirwo muzvikamu zvinoshanda zvakaita sefizikisi, economics, engineering, biology, uye computer science. Miganho inotibatsira kunzwisisa maitiro ehurongwa mumamiriro ezvinhu akaoma, kugadzira mamodheru ekufanotaura, uye kugadzirisa maitiro akasiyana-siyana. Seimwe yenheyo dzecalculus, kugona kushandisa miganhu zvinobudirira kunovhura mukana wekunzwisisa kwakadzama kwesainzi nehunyanzvi uye hunyanzvi.
