Ngā wāhanga whakatauira i roto i te pāngarau, economics me te pūtaiao rorohiko

I roto i te whakatinanatanga, tauira tauine tohu te tetahi mahere whakapakoko, hoahoa, he whakaahuatanga, he whakapakoko o te tītohunga tukanga ranei. huaina te āhuatanga ko te taketake pāngarau ranei tauira ohaoha.

He aha te mea whakatauira?

Whakatauira Ko te ako o te pūnaha ahanoa etahi. hanga hoki tona whakatinanatanga te ka tātarihia he tauira.

Katoa atamira whaihanga tā te whakamātau pūtaiao, te ahanoa o e he tauira waitara whāinga ranei. A, no te mau ana i roto i te āhuatanga motuhake o te whakamātau whakakapi i te kaupapa te tauira māmā (tārua) ranei. I roto i ētahi wā, kohikohi te tauira mahi ki tona tauira ki te matau i te huarahi o te mahi, ki te tātari i te whaihuanga ōhanga o te whakatinana i te hua o te wheako i roto i te ōhanga mākete. Ka taea te whakaaro e te taua āhuatanga rerekē tauira.

Me whiriwhiri i te kairangahau te wāhanga e tika ana o te whakatauira, te whakamahi paetahi o ratou. Ko te whakamahi o tauira e hāngai ana i roto i te wā i reira e kore e he wātea te ahanoa tūturu, ngā ki reira ranei e pā ana ki ngā raruraru taiao nui. tono te tauira o nāianei i roto i ngā āhuatanga i reira whakamātau tūturu tā nui utu pūtea.

Āhuatanga o te whakatauira pāngarau

I roto i te pūtaiao, e faufaa tauira pāngarau, me te taputapu mo ratou - ariā pāngarau. Hoki te maha tauatini, kua whiwhi ratou, hou. I roto i te pāngarau hou i reira he tikanga ao, me te kaha o te tūhuratanga. Tetahi taonga whakaaro "kuini o nga pūtaiao", tohu he tauira pāngarau. Hoki te tātaritanga āmiki o te ahanoa i tīpakohia tīpakohia ngā wāhanga o te whakatauira pāngarau. Ki te to ratou awhina wehewehe taipitopito, ngā āhuatanga, huru, codify te mōhiohio, hanga he whakaahuatanga oti o te ahanoa.

whakaōkawa Mathematical tā te whāwhā o te tūhuratanga o ngā ariā motuhake: kopu mahi, pārōnaki, tahito, tau. kua oti te tuhituhi aua whanaungatanga me ngā hononga e kore e taea e e kitea i roto i te ahanoa raro ako i waenganui i nga āhuatanga wāhanga me ngā taipitopito whanaungatanga pāngarau: whārite, rerekētanga, equalities. Ka rite ki te hua, i rite te āhuatanga whakaahuatanga pāngarau o te tukanga me te, reira, tona tauira pāngarau.

Ture o ako tauira pāngarau

He he he tetahi tikanga o kaupae whaihanga, e taea ai e koe te hanga hononga i waenga i te take me te pānga. Ko te pokapū wāhanga hoahoa o te pūnaha rangahau ko te ki te hanga i te tauira pāngarau tonu. Ko reira te kounga o te mahi whakamana i tika, tei runga i te tātaritanga atu o te ahanoa. e kore te mea he tukanga ōkawa Construction o tauira pāngarau ōhanga ranei. E tika ana kia hāneanea hoki te whakamahi, tika, e reira he kahore distortion i nga hua o te tātaritanga.

I runga i te whakarōpū o tauira pāngarau

E rua ngā momo: deterministic me stochastic tauira. tauira Deterministic whakaaro te whakatūnga o tetahi-ki-tetahi reta i waenganui i te taurangi whakamahia ki te whakaahua i te āhuatanga ahanoa ranei.

hāngai ana te huarahi taua kei i runga i te kōrero i runga i te parau tumu whakahaere o te ahanoa. I roto i te nuinga o te wā, kua he hanganga matatini te āhuatanga whakataruna, kia wetemuna e te reira te rota o te wā, me te matauranga. I roto i taua āhuatanga, kei te whiriwhiria taua wāhanga whakatauira e ka kawe i runga i nga ngā taketake, te mahi i te tukatuka o nga hua, i waho e haere ana ki te āhuatanga ariā o te ahanoa. Nuinga o ngā wā whakamahi tatauranga me te ariā tūponotanga. Ko te hua ko te tauira stochastic. I roto i te reira i reira he he hononga tupurangi i waenganui i te taurangi. He maha nui o ngā āhuatanga rerekē ko te huinga tupurangi o taurangi, āhuatanga nei i te he āhuatanga ahanoa ranei.

E whakamahia ngā wāhanga whaihanga Modern mō tauira hikohiko me te hihiri. whakaahuatanga pateko o nga momo o te whanaungatanga i waenganui i ngā taurangi tītohunga hanga kore tango ki huringa pūkete i roto i te tawhā matua o te wā. whakaahua tauira hihiri kawea nga hononga i waenganui i te taurangi e i roto i tango ki pūkete te huringa wā.

Ngā momo o tauira:

• tonu;
• motuhake;
• kākano

ngā wāhanga rerekē o te whakatauira pāngarau tukua ki a tatou te whakaahua i roto i tauira rārangi, te whanaungatanga me te mahi mā te whakamahi i te taurangi hono hāngai.

He aha e nga whakaritenga ki ngā tauira?

• Ringa rehe e. kia waiho te tauira he whakaaturanga ki tonu o nga āhuatanga katoa tūturu ki te ahanoa tūturu.
• Hāngaitanga. āhuatanga nui o te ahanoa kore e nui ake i te uara tomu'a o hapa.
• Tika. Faaite te tohu o ngā āhuatanga tāpiritanga o te ahanoa ngā i roto i te mooni, me te taua tawhā whiwhi i roto i te ako o te tauira.
• Economy. kia waiho te tauira he iti o ngā utu rauemi.

ngā wāhanga o te tauira

Ko te wāhanga matua o te whakatauira pāngarau.

• Tīpakonga Tūmahi. Whiriwhiri whāinga o te ako, tīpakohia tikanga o tona whakatinanatanga, te rautaki whakaputaina e te whakamātautau. Tenei wāhanga tā te mahi nui. Ko reira ki runga ki te tika o te mahi, tei runga i te hua mutunga o te whaihanga.

• Tātaritanga turanga ariā, Whakarāpopoto te mōhiohio riro e pā ana ki te ahanoa. he taahiraa taua tā te kōwhiringa hanganga ranei o te ariā. I roto i te ngaro o te matauranga ariā e pā ana ki te ahanoa whakapumautia causal whanaungatanga i waenganui i nga taurangi katoa tīpakohia ki te whakaahua i te āhuatanga ahanoa ranei. I tenei wā, whakatau i te hypothesize raraunga tuatahi, me te whakamutunga.
• Whakaōkawa. Kei te whakamahia ki te tīpako i te pūnaha o ngā tohu motuhake ki te āwhina i lekooti i te puka o kīanga pāngarau, te whanaungatanga i waenganui i nga wāhanga o te ahanoa.

Tāpiritanga ki te hātepe

I muri i ngā tauira tawhā tīpakohia tikanga motuhake tikanga otinga ranei.

• Whakatinanatanga o te tauira whakawhanakehia. I muri kua tīpakohia e koe pūnaha whakatauira atamira, whakaturia ake he hōtaka kei te whakamatau me e whakamahia ana ki te whakaoti i te raruraru.
• Analysis o te mōhiohio ka kohia. takoto He faaauraa i waenganui i te mahi me te otinga i whiwhi e hapa whakatauira.
• Taki te pai o te tauira ki te ahanoa tūturu. Ki te reira te mea he rerekētanga nui, whakawhanakehia te tauira hou te i waenganui ia ratou. Tae noa Na, tae noa te pai tino o te tauira ki tona orotahi tūturu, puritia whakamahine, te huri wahi.

whakatauira Āhuahira

I roto i te waenganui o te rau tau whakamutunga i roto i te ora o te tangata hou ka puta rorohiko mīhini, nui haere hāngaitanga o ngā tikanga pāngarau mō te ako o ngā me ari. He nga wāhanga pērā i "Mathematical Chemistry", "wetereo pāngarau", "economics pāngarau", oti rawa ki te ako o tītohu, ngā e i hanga e te wāhanga matua o te whakatauira.

Ratou whakaaro matua ko te matapae o te kitenga whakaritea, te ako o etahi taonga. I tua atu, ki te awhina o whaihanga e taea te ako e pā ana ki te ao, ki te titiro hoki huarahi ki te whakahaere ia ratou. A amo ana i roto i whaihanga rorohiko riro i roto i te wā i reira e kore e te whakahaere mahi i tēnei wā. I muri hanga he tauira pāngarau o te āhuatanga i raro i ako i te tikanga o whakairoiro rorohiko taea ako pahūtanga karihi, te whiu me te pera i runga i. D.

te tāutu i ngā tohunga e toru ngā wāhanga o te whakatauira pāngarau, me he ia ona ake āhuatanga:

• Construction o te tauira. Tenei wāhanga Ko tā te mahi o te mahere ōhanga, te ari o te natura, hoahoa, production tukanga. Mārama whakaahua Ko uaua te āhuatanga i roto i tenei take. Tuatahi e hiahia ana koe ki te tautuhi i te pū o te tītohunga, ki te whakatau i te hononga i waenganui i reira, me te tahi atu taonga. Na e whakamaoritia nga āhuatanga kounga katoa ki te reo pāngarau, hanga he tauira pāngarau. Ko te uaua tino i roto i te tukanga katoa o te whakatauira tenei atamira.
• otinga wāhanga o te raruraru pāngarau e pā e te ki te whanaketanga o hātepe, tikanga o whakaoti te raruraru i runga i te hangarau rorohiko, te tāututanga o ngā hapa inenga.
• Translation o te mōhiohio riro i te akoranga o rangahau i roto i te reo o te rohe mo i whakahaere te whakamātau i.

E whakareia ana e manatoko o te pai o te tauira hua toru enei ngā wāhanga o te whakatauira pāngarau. Ka taki i te ōritetanga i waenganui i te hua whiwhi i roto i te whakamātautau ki te matauranga ariā. Ki te tika, he whakarereke o te tauira hanga. Haafifi faaohie i te reira ranei, i runga i te hua rānei.

whakatauira Rawa ōhanga

ngā 3 takahanga te whakamahi o te whakatauira pāngarau o taurangi, whārite pārōnaki. Hanga taonga matatini te whakamahi i kauwhata ariā. Ko tā te reira i te huinga o ngā i roto i te wāhi ranei i runga i te wahi rererangi rara tūhono. Ko te wāhanga matua o te whakatauira ōhanga ee momo o rauemi, ratou tohatoha, tango ki waka pūkete, whakamahere whatunga. e kore te mea aha mahi he taahiraa i roto i te whaihanga? He uaua ki te pahono i teie uiraa unambiguously, reira katoa tei runga i te āhuatanga motuhake. Ko te wāhanga matua o te tukanga whakatauira riro take waihanga me te rangahau kaupapa, kōwhiringa o ngā āhuatanga taketake ki te whakatutuki i te whakaaro, te hononga i waenganui i te whakaahuatanga o te tauira whatiwhatinga. E whakamana mā te whakamahi i ngā tātai pāngarau atu tātaitanga.

Hei tauira, ratonga ariā ko te raruraru o te tāpae. He mea nui ki te kitea he toenga i waenganui i te utu o nga whakaaro, me te ihirangi ki noho i roto i te utu rārangi. I muri hanga he whakaahuatanga ōkawa o te tātaitanga tauira kawea atu te whakamahi i te tikanga tātai, me te tātari. Ka taea e kitea e koe e tali ki te pātai katoa i roto i te tauira waihanga kounga. Ki te he kino te tauira, e kore e taea ki te mārama me pēhea te kore ko te mahi he taahiraa i roto i te whaihanga.

Māmā ko te paearu pono mō te aromātai i te pai o te āhuatanga tauira ranei. tauira Multicriteria, tae atu i te kōwhiringa arotautanga, te whakaaro tikanga o te waihanga. Ko te ara ki te whakatutuki i tenei he rerekē. I roto i te fifi e te hunga ka taea i roto i te tukanga, kia miramira:

• i roto i te pūnaha matatini i waenganui i nga mea timatanga, i reira e rave rahi hononga;
• Ko reira uaua ki te tango ki roto ki pūkete nga āhuatanga tupurangi katoa, te tātari i te pūnaha tūturu;
• uaua ki te whakarite i te taputapu pāngarau ki nga hua e hiahia ana koe ki te tiki

No te mea o te mau fifi e rave rahi e ara ake i roto i te tukanga o ako nga pūnaha multidimensional, kua whakawhanakehia whaihanga kua. E pā ana te reira ki te huinga o ngā hōtaka motuhake mō ngā rorohiko, e whakaahua ana i te mahi o nga āhuatanga takitahi o te pūnaha, me te hononga i waenganui i a ratou. Ko te whakamahi o ngā taurangi matapōkere tā te tāruarua o ngā, tukatuka tatauranga o ngā hua. Te mahi ki te pūnaha whaihanga ko te whakamātau kawea e te roto i te taha o te tikanga o te rorohiko. He aha e nga painga o tenei pūnaha? Waihoki, ka taea e koe te whakatutuki pātata nui ki te pūnaha tūturu, e kore e taea i roto i te take o te tauira pāngarau. Mā te whakamahi i te poraka taea parau tumu ki te tātari poraka takitahi i mua i e whakaurua ratou ki roto ki te pūnaha kotahi. Taua te kōwhiringa ka taea te whakamahi o ririki matatini e kore e taea te whakaahuatia e te whanaungatanga pāngarau tikanga.

I roto i te āhuatanga o te pūnaha whaihanga, tohatoha utu i roto i te wa, me ngā rauemi, me te te hiahia ki te whakamahi i te hangarau rorohiko hou.

Ngā wāhanga o te whanaketanga o te whaihanga i rite nei ki nga huringa tango wahi i roto i te hapori. I runga i te whakamahi o tauira katoa kua wehea ki ngā hōtaka whakangungu, kaiwhakangungu, taonga ataata mātauranga. Ka taea te heke Momo kape o ngā tūturu (waka). taatou pūtaiao me te hangarau he turanga hanga mo te hikohiko tātari. tauira whaihanga e kore anake whakaata te mooni reira, amo whakamatauria ratou i runga i kiore taiwhanga, ngā i roto i te pūnaha mātauranga. kite ia peehia te rite te tikanga o te tamataraa, me te hapa.

He he he wehenga o tauira katoa o te kōwhiringa aroaro. E huaina tauira tinana lalahi. E hua ana taua rerekē ki ngā āhuatanga āhuahanga, me te tinana o te taketake, e taea te iritihia ratou ki mooni. tauira Information e taea ki te pa ki. tohu ratou te kāwanatanga me ngā āhuatanga o te ahanoa ako, tītohunga, tukanga, ka kōrero ratou ki te ao tūturu. kōwhiringa kōrero ngā tauira kōrero whakatinana i roto i te puka o te kōrero hinengaro ranei. matamaha whakaaro rongonui whakahuatia e te whakamahi o etahi tohu reo pāngarau.

mutunga

puta wā kotahi whakatauira Mathematical rite te tikanga o te matauranga pūtaiao ki te taketake o te pāngarau teitei. He wāhi nui i roto i te tukanga taua i takaro e Ihaka Newton, Descartes, Leibniz. I te tuatahi i hanga tauira Mathematical Fermat, B. Pascal. whakatauira Mathematical i roto i te hanga, utua ōhanga whakarongo V. V. Leontev, vv Novozhilov, A. L. maimoa. I teie mahana, whakamahia he kē rite o te ahanoa o ako tetahi tītohunga e i roto i ngā ao o te mahi. Ki te pūnaha hangaia Engineers tūhura taua ari me ngā tukanga e kore e taea te tātarihia i roto i ngā āhuatanga tūturu.

Rangahau i te whakatauira whakamahia i roto i nga wa onamata, pae hopea hopu ngā momo o te matauranga pūtaiao: architecture, engineering, matū, hanga, ahupūngao, te koiora, rauropi, geography, me rangahau pāpori. I roto i tetahi whakatauira tukanga whakamahi toru huānga: kaupapa, ahanoa, tauira. O te akoranga, e kore te te ako whaihanga o te ahanoa tītohunga ranei iti ki, i reira e te tahi atu mau rave'a ki te whiwhi i te mōhiohio e tika ana.