Kugwiritsa Ntchito Zochokera M'magawo Osiyanasiyana a Sayansi
Chochokera ku chinthuchi ndi lingaliro lofunikira mu calculus, lomwe linayambitsidwa ndi Sir Isaac Newton ndi Gottfried Wilhelm Leibniz kumapeto kwa zaka za m'ma 17. Mu masamu, chochokera ku chinthuchi chimayimira kusintha kwa ntchito poyerekeza ndi chimodzi mwa zinthu zake. Lingaliroli silili lofunikira pa masamu okha komanso limagwiritsidwa ntchito kwambiri m'magawo ena osiyanasiyana a sayansi. Nkhaniyi ifotokoza za kugwiritsa ntchito kosiyanasiyana kwa zochokera ku chinthuchi m'magawo osiyanasiyana, kuyambira pa fizikisi ndi zachuma mpaka biology ndi uinjiniya mpaka sayansi ya makompyuta.
1. Fiziki
Ma derivatives ndi ofunikira kwambiri mu fizikisi, makamaka mu makina akale. Chimodzi mwa zitsanzo zoyambira ndi ubale pakati pa malo, liwiro, ndi kufulumira. Ngati \( s(t) \) ndi malo a chinthu monga nthawi, ndiye kuti:
– Liwiro (\( v(t) \)) ndiye chiyambi choyamba cha malo ponena za nthawi: \( v(t) = \frac{ds(t)}{dt} \).
– Kuthamanga (\( a(t) \)) ndi chiyambi choyamba cha liwiro kapena chiyambi chachiwiri cha malo ponena za nthawi: \( a(t) = \frac{dv(t)}{dt} = \frac{d^2s(t)}{dt^2} \).
Kuphatikiza apo, mu electromagnetism, lamulo la Faraday la induction ya electromagnetic limati mphamvu ya electromotive (EMF) yomwe imachitika mu circuit ndi yochokera ku magnetic flux ponena za nthawi.
2. Zachuma
Mu zachuma, zinthu zochokera kuzinthu zina zimagwiritsidwa ntchito pofufuza kusintha kwa mtengo, ndalama, ndi ntchito zopangira. Mwachitsanzo:
– Mtengo Wapambali (Biaya Marginal) ndi chochokera ku ntchito yonse ya mtengo poyerekeza ndi kuchuluka kwa zotuluka, zomwe zimasonyeza momwe ndalama zonse zimasinthira pamene kupanga kukuwonjezeka: \( MC = \frac{dTC}{dQ} \).
– Ndalama Zochepa (Ndalama Zochepa) ndi zomwe zimachokera ku ntchito yonse ya ndalama zokhudzana ndi kuchuluka kwa zomwe zatuluka, zomwe zimafotokoza ndalama zowonjezera pamene malonda akuwonjezeka: \( MR = \frac{dTR}{dQ} \).
Ntchito ina yofunika kwambiri ndi mu chiphunzitso cha utility. Ntchito ya utility imafotokoza kukhutitsidwa kapena kugwiritsidwa ntchito komwe kumapezeka kuchokera ku kugwiritsidwa ntchito kwa katundu ndi mautumiki. Chochokera choyamba cha ntchito ya utility chimatchedwa marginal utility, chomwe chimasonyeza kukhutitsidwa kowonjezereka komwe kumapezeka kuchokera kukugwiritsa ntchito gawo lina la chinthu kapena ntchito.
3. Zamoyo
Mu biology, zotumphukira zimagwiritsidwa ntchito potengera njira zosiyanasiyana zosinthira. Mwachitsanzo, mu ecology, zitsanzo za kukula kwa anthu nthawi zambiri zimagwiritsa ntchito zotumphukira pofotokoza kuchuluka kwa kukula kwa anthu. Zitsanzo za kukula kwa anthu ndi zodziwika bwino ndi zitsanzo ziwiri:
– Chitsanzo cha kukula kwa zinthu: \( \frac{dN}{dt} = rN \), pomwe \(N \) ndi kukula kwa anthu ndipo \(r \) ndi kuchuluka kwa kukula kwa zinthu.
– Chitsanzo cha kukula kwa zinthu: \( \frac{dN}{dt} = rN \left( 1 – \frac{N}{K} \right) \), pomwe \( K \) ndi mphamvu ya chilengedwe ndipo \( \left( 1 – \frac{N}{K} \right) \) ndi chinthu chochepetsa chomwe chimachepetsa kuchuluka kwa kukula pamene mphamvu ya chilengedwe ikuyandikira.
Mu fiziyoloji, zinthu zochokera m'thupi zimagwiritsidwa ntchito potengera njira za thupi monga kuyenda kwa magazi ndi kutumiza kwa zizindikiro za mitsempha. Mwachitsanzo, lamulo la Darcy la kuyenda kwa magazi m'mitsempha yamagazi limagwiritsa ntchito zinthu zochokera m'thupi pofotokoza kusintha kwa kuthamanga kwa magazi m'mitsempha.
4. Njira
Zotumphukira nazonso ndizofunikira kwambiri m'magawo osiyanasiyana a uinjiniya. Mu uinjiniya wa zomangamanga ndi makanika, zotumphukira zimagwiritsidwa ntchito mu kusanthula kapangidwe ka zinthu ndi makina amadzimadzi. Mwachitsanzo:
– Mu kusanthula kapangidwe ka zinthu, njira ya finite element imagwiritsidwa ntchito kudziwa masinthidwe ndi kupsinjika kwa zinthu m'mapangidwe. Chochokera ku ntchito yosuntha chimapereka kupsinjika, ndipo chochokera ku kupsinjikako chimapereka kupsinjika.
– Mu njira yogwiritsira ntchito madzi, ma equation a Navier-Stokes amafotokoza kayendedwe ka madzi. Ma equation awa ndi ma equation osiyana omwe amaphatikizapo zotumphukira pang'ono za liwiro la madzi poyerekeza ndi nthawi ndi malo.
Mu uinjiniya wamagetsi, ma derivatives amagwiritsidwa ntchito pofufuza ma circuit amagetsi. Malamulo a Kirchhoff ndi chiphunzitso cha netiweki nthawi zambiri amagwiritsa ntchito ma derivatives pofotokoza ubale womwe ulipo pakati pa mphamvu yamagetsi, magetsi, ndi inductance m'ma circuit amagetsi.
5. Sayansi ya Pakompyuta
Mu sayansi ya makompyuta, ma derivatives amagwiritsidwa ntchito pokonza ndi kuphunzira makina. Chimodzi mwa ntchito zazikulu ndi mu ma algorithms optimization monga gradient descent. Algorithm iyi imagwiritsidwa ntchito kuchepetsa mtengo mu njira yophunzitsira ya makina ophunzirira:
- Gradient ndiye vector yoyamba yochokera ku ntchito ya mtengo poyerekeza ndi magawo a chitsanzo, zomwe zimasonyeza komwe kusintha kwakukulu kukupita.
- Kutsika kwa ma gradient ndi njira yobwerezabwereza yomwe imagwiritsa ntchito ma gradient kuti isinthe magawo a chitsanzo kuti afike pa ntchito yotsika mtengo.
Kuphatikiza apo, mu zithunzi za pakompyuta, zinthu zochokera ku zinthu zina zimagwiritsidwa ntchito kusintha kuwala ndi mithunzi. Lamulo la Lambert ndi chitsanzo cha kuwala kwa Phong zimagwiritsa ntchito zinthu zochokera ku zinthu zina kuti ziwerengere mphamvu ya kuwala komwe kumaonekera kuchokera pamwamba pomwe kuwala kumapezeka.
6. Mankhwala
Mu chemistry, ma derivatives amagwiritsidwa ntchito mu reaction kinetics pofotokoza liwiro la chemical reaction. Nthawi zambiri reaction rate imafotokozedwa ngati derivative ya kuchuluka kwa reactant kapena mankhwala poyerekeza ndi nthawi. Mwachitsanzo, pa reaction yoyamba:
\[ \text{Reactants} \rightarrow \text{Products} \]
Mlingo wa reaction rate (r(t)) ukhoza kufotokozedwa motere:
\[ r(t) = – \frac{d[\text{Reactant}]}{dt} = \frac{d[\text{Product}]}{dt} \]
Kuphatikiza apo, ma derivatives amagwiritsidwa ntchito mu thermodynamics pofufuza kusintha kwa mphamvu mu dongosolo. Mwachitsanzo, mphamvu ya Gibbs free (G) ndi ntchito ya thermodynamic yomwe nthawi zambiri imagwiritsidwa ntchito kulosera komwe mankhwala amachitikira, ndipo derivative yoyamba ya G pokhudzana ndi madigiri a ufulu wa dongosolo imapereka chidziwitso chokhudza momwe thermodynamic imagwirira ntchito.
Mapeto
Kuchokera pakufotokozera pamwambapa, n'zoonekeratu kuti lingaliro la zotumphukira limagwiritsidwa ntchito kwambiri m'magawo osiyanasiyana asayansi. Mu fizikisi, zotumphukira zimafotokoza ubale wofunikira pakati pa malo, liwiro, ndi kufulumira. Mu zachuma, zotumphukira zimagwiritsidwa ntchito pofufuza ndalama zochepa ndi ndalama zomwe zimapezedwa. Mu biology, zotumphukira zimathandiza kutsanzira kukula kwa anthu ndi njira za thupi. Mu uinjiniya, zotumphukira ndizofunikira pakusanthula kapangidwe ka zinthu ndi makina amadzimadzi. Sayansi ya makompyuta imagwiritsa ntchito zotumphukira mu ma algorithms optimization ndi kuphunzira kwa makina. Mu chemistry, zotumphukira zimagwiritsidwa ntchito mu reaction kinetics ndi thermodynamics. Chifukwa chake, kumvetsetsa ndi kudziwa bwino lingaliro la zotumphukira ndikofunikira kwa asayansi ndi mainjiniya m'magawo osiyanasiyana.
