Ukusetshenziswa Kwezinto Ezivela Kuyo Esayensini Nasebuchwephesheni
I-derivative ingumqondo oyisisekelo ekubaleni osetshenziswa kabanzi emikhakheni ehlukahlukene yesayensi nobuchwepheshe. I-derivative ilinganisa ukuthi umsebenzi ushintsha kanjani njengoba okokufaka kwawo kushintsha. Lesi sihloko sizoxoxa ngokusetshenziswa okuhlukahlukene kwe-derivatives emikhakheni ebalulekile njenge-physics, ezomnotho, i-biology, ubunjiniyela, kanye nesayensi yekhompyutha, kanye nezindlela ezisebenzayo zokuzisebenzisa empilweni yansuku zonke.
Ifiziksi
Ku-physics, ama-derivatives asetshenziswa kabanzi ukubala ijubane kanye nokusheshisa kwezinto ezihambayo. Njengomfanekiso, uma indawo yento inikezwa umsebenzi \( s(t) \) oncike esikhathini \(t \), khona-ke ijubane \( v(t) \) liyi-derivative yokuqala yesikhundla, okungukuthi, \( v(t) = \frac{ds}{dt} \). Ukusheshisa kuyi-derivative yesibili yesikhundla noma i-derivative yokuqala yejubane, okungukuthi, \( a(t) = \frac{dv}{dt} = \frac{d^2s}{dt^2} \).
Ngaphezu kwalokho, ama-derivatives asetshenziswa futhi kuma-mechanics akudala ukuhlaziya ukunyakaza okulula kwe-harmonic, njengokunyakaza kwentwasahlobo kanye nokudlidliza kwe-pendulum. Ku-theory ye-electromagnetic, izibalo eziyisisekelo zikaMaxwell zamasimu kagesi namagnetic nazo zisebenzisa ama-derivative angaphelele ukuveza ukwehluka kwamasimu esikhaleni nasesikhathini.
umnotho
Ama-derivative asetshenziswa kabanzi kwezomnotho ukuhlaziya izinguquko eziguquguqukayo zomnotho. Isibonelo, uma sinomsebenzi wezindleko eziphelele \( C(q) \) oncike enanini lomkhiqizo \( q \), khona-ke i-derivative yokuqala yalo msebenzi wezindleko \( C'(q) \) inikeza izindleko ezingaphansi, okuyizindleko ezengeziwe zokukhiqiza iyunithi eyodwa eyengeziwe yomkhiqizo. Ngokufanayo, umsebenzi wenzuzo \( \pi(q) \) ungahlukaniswa ukuze kutholakale inzuzo engaphansi, okubonisa ukuthi izinguquko ezincane enanini lomkhiqizo zingathinta kanjani inzuzo ephelele.
Ukuqonda umqondo wezinto ezisuselwe kuzo kusiza osomnotho ukuthi benze ukuhlaziywa kokuthuthukisa, njengokunquma inani lokukhiqiza elikhulisa inzuzo noma imali engenayo. Lokhu kubalulekile ekuhleleni ibhizinisi kanye nokwenza izinqumo.
I-Biologi
Ku-biology, ama-derivatives asetshenziswa kumamodeli ahlukahlukene ezibalo achaza izinqubo ze-biology. Isibonelo esisodwa esibalulekile yimodeli yokukhula kwabantu. Kumodeli yokukhula kwe-exponential, ushintsho kubantu \( P(t) \) luvezwa njenge \( \frac{dP}{dt} = kP \), lapho \( k \) kuyisilinganiso sokukhula. Lesi sibalo somehluko singahlanganiswa ukuze kutholakale umsebenzi \( P(t) \) ochaza abantu ngesikhathi esithile.
Ama-derivatives asetshenziswa futhi ekuqondeni i-enzyme dynamics ekuphenduleni kwamakhemikhali, ngokusebenzisa i-Michaelis-Menten equation, ehlobanisa amazinga okusabela nokugxila kwe-substrate. Izazi ze-Biomathematics zisebenzisa ama-derivatives ukukhombisa ukusabalala kwesifo, ukusebenzisana kwezilwane ezidla ezinye izilwane, kanye nezinye i-ecosystem dynamics.
lobuchwepheshe
Kubunjiniyela, ama-derivatives asetshenziswa ekuhlaziyweni kwezinhlelo ezishintshashintshayo, ukulawula okuzenzakalelayo, nokuningi. Ekuhlaziyweni kwezinhlelo ezishintshashintshayo, ama-equation aqondile kanye nangaphandle komugqa asetshenziswa ukuchaza ukuziphatha kwezinhlelo ze-mechanical, kagesi, ezishisayo, nezinye. Isibonelo, ekuhlaziyweni kwesekethe kagesi, iMithetho kaKirchhoff iveza ama-equation ahlukile abese exazululwa ukuze kuqondwe izinguquko ze-voltage kanye nezamanje.
Kubunjiniyela bokulawula okuzenzakalelayo, ama-derivatives asetshenziswa ukuklama abalawuli be-PID (Proportional-Integral-Derivative). Laba balawuli babalulekile ekulawuleni izinhlelo zezimboni ukuqinisekisa ukuthi umphumela wesistimu uhambisana nokufakwayo okufunwayo. Abalawuli be-PID basebenzisa ulwazi oluvela ephutheni lamanje (P), ephutheni elidlule (I), kanye nesilinganiso sokushintsha kwephutha (D).
Isayensi yekhompyutha
Kusayensi yekhompyutha, umqondo we-derivatives usetshenziswa ngokusobala kakhulu ekufundeni komshini, ikakhulukazi ekwenzeni ngcono okusekelwe ku-gradient. I-algorithm ye-gradient desccent, esetshenziselwa ukwenza ngcono amanethiwekhi e-neural artificial, ihilela ukubala i-partific derivatives yomsebenzi wokulahlekelwa maqondana nepharamitha ngayinye yemodeli. Le nqubo isiza ekutholeni amanani epharamitha afanele anciphisa ukulahlekelwa futhi athuthukise ukusebenza kwemodeli.
Ngaphezu kwalokho, kuma-computer graphics, ama-derivatives asetshenziswa ekufakeni izithunzi kanye nokuveza ukuze kukhiqizwe imiphumela yokukhanya engokoqobo. Isibonelo, okujwayelekile kwezindawo ezisetshenziswa ekufakeni izithunzi ze-Phong kubalwa kusetshenziswa ama-derivatives angaphelele emisebenzi echaza lezo zindawo.
Izicelo Empilweni Yansuku Zonke
Ngaphandle kokusetshenziswa kwayo emikhakheni yezemfundo neyobungcweti, ama-derivatives nawo asetshenziswa ngokunganakile empilweni yansuku zonke. Isibonelo, lapho sishayela, siyaqonda ngokusobala imiqondo yesivinini kanye nokusheshisa; singahlola ngokuzenzakalelayo izinguquko zesivinini kanye nebanga ngokuhamba kwesikhathi.
Kwezezimali zomuntu siqu, ukuqonda izinguquko zesilinganiso senzalo kanye nomthelela wazo emalinimboleko nasekutshalweni kwezimali nakho kuyindlela ewusizo yokusebenzisa izinto ezisuselwe kuzo. Ngokufanayo, ekuphekeni, izinga lokushintsha kwezinga lokushisa lesitsha ngokuhamba kwesikhathi lingabalwa ukuze kukhiqizwe isitsha esiphelele.
Ukusetshenziswa Okungokoqobo Kwezinto Ezivela Kuzona: Izibonelo Zezimo
Ekuphetheni, sizoxoxa ngesibonelo sangempela esibonisa ukusetshenziswa okungokoqobo komqondo osuselwe kokunye. Ake sithi sifuna ukunciphisa isikhathi sokuhamba emzileni othile ngesivinini esinqunyelwe esihlukahlukene.
Sinomsebenzi wesikhathi sokuhamba \( T(x) \) oncike kwijubane \( x \). Sisebenzisa indlela ye-derivatives, singathola ijubane elifanele \( x \) elinciphisa isikhathi sokuhamba. Le nqubo ihilela:
1. Nquma umsebenzi \( T(x) \).
2. Bala i-derivative yokuqala \( \frac{dT}{dx} \).
3. Linganisa \( \frac{dT}{dx} = 0 \) bese uthola inani lika \( x \).
4. Sebenzisa i-derivative yesibili ukuqinisekisa ukuthi inani le-\( x \) linciphisa isikhathi sokuhamba.
Ezimweni eziyinkimbinkimbi kakhulu, isibonelo ekusesheni indlela emfushane kakhulu kusetshenziswa i-algorithm A, umqondo we-derivatives usetshenziswa ekubalweni kwe-heuristic ukulinganisa izindleko zokuhamba usuka endaweni eyodwa uye kwenye.
Isiphetho
Ama-derivatives angamathuluzi anamandla futhi anokuguquguquka asetshenziswa emikhakheni eminingi yesayensi kanye nezicelo ezisebenzayo. Kusukela ku-physics kuya kwezomnotho, i-biology kuya kobunjiniyela, ngisho nesayensi yekhompyutha, ikhono lokuqonda nokusebenzisa ama-derivatives livumela ochwepheshe ukuthi benze izibikezelo ezinembile, bathuthukise imiphumela, futhi baxazulule izinkinga eziyinkimbinkimbi. Ukuqonda kahle lo mqondo kuvula amathuba amaningi okusungula izinto ezintsha kanye nentuthuko eyengeziwe emikhakheni ehlukahlukene yesayensi nobuchwepheshe.
