Mashandisirwo eZvinhu Zvakatorwa Muminda Yakasiyana-siyana yeSainzi
Chinobva pazviri ipfungwa huru mukuverenga, yakaunzwa naSir Isaac Newton naGottfried Wilhelm Leibniz mukupera kwezana remakore rechi17. Mumasvomhu, chinobva pazviri chinomiririra mwero wekuchinja kwebasa maererano nechimwe chezvinhu zvarinoshandura. Pfungwa iyi haisi chete yakakosha kumasvomhu asiwo ine mashandisirwo akawanda mune mamwe maindasitiri esainzi. Chinyorwa chino chichakurukura mashandisirwo akasiyana-siyana emaderivatives muzvikamu zvakasiyana-siyana, kubva pafizikisi nehupfumi kusvika kubiology neinjiniya kusvika kusayenzi yekombuta.
1. Fizikisi
Zvinobva pane chimwe chinhu zvakakosha zvikuru mufizikisi, kunyanya mu classical mechanics. Imwe yemienzaniso mikuru ndeye hukama huripo pakati penzvimbo, velocity, uye acceleration. Kana \( s(t) \) iri nzvimbo yechinhu sebasa renguva, saka:
– Kumhanya (\( v(t) \)) ndicho chinhu chekutanga chinobva panzvimbo maererano nenguva: \( v(t) = \frac{ds(t)}{dt} \).
– Kukurumidza (\( a(t) \)) iderivative yekutanga yevelocity kana derivative yechipiri yenzvimbo maererano nenguva: \( a(t) = \frac{dv(t)}{dt} = \frac{d^2s(t)}{dt^2} \).
Pamusoro pezvo, mu electromagnetism, mutemo waFaraday we electromagnetic induction unotaura kuti simba re electromotive (EMF) rinokonzerwa mu circuit ndiro rinobva mu magnetic flux maererano nenguva.
2. Hupfumi
Muzvehupfumi, maderivatives anoshandiswa kuongorora shanduko mumitengo, mari inowanikwa, uye mabasa ekugadzira. Semuenzaniso:
– Mari yeMarginal (Biaya Marginal) ishoko rinobva pabasa remutengo wezvose maererano nehuwandu hwezvinobuda, izvo zvinoratidza kuti mitengo yese inoshanduka sei sezvo kugadzirwa kuchiwedzera: \( MC = \frac{dTC}{dQ} \).
– Mari Yemari ...
Imwe nzira inokosha yekushandisa iri mudzidziso yekushandiswa kwezvinhu. Basa rekushandiswa rinotsanangura kugutsikana kana kushandiswa kwezvinhu nemasevhisi. Chinobva pakutanga chebasa rekushandiswa kwezvinhu chinonzi marginal utility, icho chinoratidza kugutsikana kwakawedzerwa kunowanikwa nekushandisa imwe unit yechinhu kana sevhisi.
3. Biology
Mubiology, maderivatives anoshandiswa kutevedzera maitiro akasiyana-siyana anochinja-chinja. Semuenzaniso, mu ecology, mamodel ekukura kwevanhu anowanzo shandisa maderivatives kutsanangura mwero wekukura kwevanhu. Mamodel ekukura kwe exponential ne logistic imhando mbiri dzakajairika:
– Exponential growth model: \( \frac{dN}{dt} = rN \), apo \( N \) iri huwandu hwevanhu uye \( r \) iri huwandu hwekukura kwemukati.
– Logistic growth model: \( \frac{dN}{dt} = rN \left( 1 – \frac{N}{K} \right) \), apo \( K \) ndiyo nharaunda ine simba uye \( \left( 1 – \frac{N}{K} \right) \) ndiyo inoderedza kukura kwenzvimbo.
Mu physiology, zvinhu zvinobuda mumuviri zvinoshandiswa kutevedzera maitiro emuviri akadai sekuyerera kweropa uye kutapurirana kwezviratidzo zvetsinga. Semuenzaniso, mutemo waDarcy wekuyerera kweropa mutsinga dzeropa unoshandisa zvinhu zvinobuda mumuviri kutsanangura shanduko mukumanikidzwa kweropa mutsinga.
4. Maitiro ekugadzira
Zvigadzirwa zvemhando yepamusoro zvakakoshawo zvikuru muzvikamu zvakasiyana-siyana zveinjiniya. Muinjiniya yezvivakwa uye makanika, zvigadzirwa zvemhando yepamusoro zvinoshandiswa mukuongorora chimiro uye mukugadzira kwemvura. Semuenzaniso:
– Mukuongorora chimiro, nzira ye finite element inoshandiswa kuona deformations uye stress mu structures. Derivative ye displacement function inopa strain, uye derivative ye strain inopa stress.
– Mukuongorora fluid mechanics, Navier-Stokes equations inotsanangura fluid flow. Aya equation idifferential equations inosanganisira partial derivatives yefluid velocity maererano nenguva nenzvimbo.
Muinjiniya yemagetsi, madhirivhiti anoshandiswa mukuongorora madhirivhiti emagetsi. Mitemo yaKirchhoff nedzidziso yenetwork zvinowanzo sanganisira madhirivhiti kutsanangura hukama huripo pakati pemagetsi, voltage, uye inductance mumadhirivhiti emagetsi.
5. Sainzi yeKombuta
Musainzi yemakombiyuta, ma derivatives anoshandiswa mukugadzirisa uye mukudzidza kwemuchina. Imwe yemashandisirwo makuru ndeyekugadzirisa ma algorithms akadai se gradient descent. Iyi algorithm inoshandiswa kuderedza mutengo mukudzidziswa kwemuchina wekudzidza:
- Gradient ndiyo yekutanga derivative vector ye cost function maererano nema model parameters, izvo zvinoratidza divi rekuchinja kukuru.
- Kudzika kweGradient inzira inodzokororwa inoshandisa magradients kugadzirisa ma parameter emuenzaniso kusvika pamutengo wakaderera.
Pamusoro pezvo, mumagirafu emakombiyuta, maderivatives anoshandiswa kugadzirisa chiedza nemimvuri. Mutemo waLambert nePhong lighting model zvinoshandisa maderivatives kuverenga simba rechiedza rinoonekwa kubva pamusoro pechiedza.
6. Kemikari
Mukemikari, maderivatives anoshandiswa mu reaction kinetics kutsanangura mwero we chemical reaction. Muwero we reaction unowanzo tsanangurwa se derivative ye concentration ye reactant kana chigadzirwa maererano nenguva. Semuenzaniso, kune reaction yekutanga:
\[ \text{Reactants} \rightarrow \text{Products} \]
Chiyero che reaction \( r(t) \) chinogona kuratidzwa seizvi:
\[ r(t) = – \frac{d[\text{Reactant}]}{dt} = \frac{d[\text{Product}]}{dt} \]
Pamusoro pezvo, ma derivatives anoshandiswa mu thermodynamics kuongorora shanduko dzesimba musystem. Semuenzaniso, Gibbs free energy (G) ibasa re thermodynamic rinowanzo shandiswa kufanotaura mafambiro emakemikari, uye derivative yekutanga yeG maererano nemadhigirii erusununguko rwesystem inopa ruzivo nezve mamiriro e thermodynamic equilibrium.
Mhedziso
Kubva pane tsananguro iri pamusoro apa, zviri pachena kuti pfungwa yezvinobuda muzvinhu ine mashandisirwo akawanda muzvikamu zvakasiyana-siyana zvesainzi. Mufizikisi, zvinobuda muzvinhu zvinotsanangura hukama hwakakosha pakati penzvimbo, kumhanya, uye kukurumidza. Muhupfumi, zvinobuda muzvinhu zvinoshandiswa kuongorora mari shoma nemari inowanikwa. Mubiology, zvinobuda muzvinhu zvinobatsira kuratidza kukura kwevanhu uye maitiro emuviri. Muinjiniya, zvinobuda muzvinhu zvinokosha mukuongorora kwechimiro uye fluid mechanics. Sainzi yemakombiyuta inoshandisa zvinobuda mukugadzirisa maalgorithms uye kudzidza kwemuchina. Mukemistri, zvinobuda muzvinhu zvinoshandiswa mu reaction kinetics uye thermodynamics. Naizvozvo, kunzwisisa nekuziva pfungwa yezvinobuda muzvinhu zvakakosha kune masayendisiti nemainjiniya muzvikamu zvakasiyana-siyana.
