Kalam lambobin: kirga hanyoyin da misalai

Zai yiwu manufar wanda aka samu shi ne saba wa dukan mu tun makarantar sakandare. Yawancin lokaci dalibai da wahala fahimtar wannan ne babu shakka mai da muhimmanci sosai abu. An rayayye amfani a fannoni daban daban na rayuwar mutane, kuma da yawa injiniya aka tushen daidai a kan ilmin lissafi lissafin samu da wanda aka samu. Amma kafin a ci gaba zuwa wani bincike na abin da yake a wanda aka samu da lambobi, kamar yadda suka lissafi da kuma inda za su zo a cikin m, delve kadan cikin tarihi.

labarin

A ra'ayi na wanda aka samu, wanda shi ne tushen ilmin lissafi analysis, ya bude (ko da mafi alhẽri a ce "ƙirƙira" domin shi ne, kamar yadda irin wannan, ba ya wanzu a yanayi) Isaakom Nyutonom, wanda mun san daga gano dokar nauyi. Shi ya fara amfani da wannan ra'ayi a cikin kimiyyar lissafi ga nauyin halitta na gudu da kuma hanzari na jikinsu. Kuma masana kimiyya da dama har yanzu yabon Newton ga wannan gagarumin ƙarya, saboda a gaskiya ya ƙirƙira tushen bambanci da na game ilimin lissafi, da gaskiyane tushen dukan fannin lissafi da ake kira "ilmin lissafi bincike". Ko a lokacin da Nobel Prize, Newton m dã sun samu da shi 'yan sau.

Ba tare da sauran manyan hankulansu. Bugu da kari ga Newton a kan ci gaban wanda aka samu da kuma na game aiki irin mashawarta yan baiwa na lissafi kamar yadda Leonhard Euler, Lagrange da kuma Louis Gotfrid Leybnits. Shi ne da godiya ga su da muke da ka'idar bambanci ilimin lissafi a cikin nau'i a wadda ta wanzu har ya zuwa yau. Ba zato ba tsammani, wannan shi ne Leibniz gano lissafi ma'anar wanda aka samu, wanda bai kasance kõme ba fiye da gangaren tangent zuwa jadawali na aiki.

Mene ne wani wanda aka samu da lambobin? Bit sake abin da ya faru a cikin makaranta.

Mene ne wani wanda aka samu?

Ƙayyade wannan ra'ayi a cikin da dama hanyoyi daban-daban. A mafi sauki bayani: Kalam - shi ne da yawan canzawar aiki. Wakilci jadawali na wani aiki y na x. Idan ba a mike, yana da wasu masu lankwasa a cikin jadawali, da lokaci na karuwa kuma yana raguwa. Idan ka dauki kowane infinitesimal tazara na jadawali, shi zai zama wani madaidaiciya line kashi. Saboda haka, da rabo daga cikin size of wani infinitesimal kashi na y ga girman da x daidaita, kuma zai kasance wani wanda aka samu daga cikin aikin a iyakancen lokaci. Idan muka yi la'akari da aiki a matsayin dukan, maimakon a wata takamaiman ma'ana, mun samu wani aiki na wanda aka samu, watau a wasu dogara a kan X y.

Bugu da kari, baya daga jiki ma'anar wanda aka samu a matsayin aiki na da yawan canzawar, akwai kuma wani lissafi da hankali. A nan, za mu yanzu tattauna.

A lissafi ma'anar

Kalam lambobin da kansu su ne wani adadi da ba ta dace fahimtar ba ya gudanar da wani ma'ana. Sai dai itace cewa da wanda aka samu ba kawai ya nuna ci gaban da kudi ko rage aiki, kuma gangaren tangent zuwa jadawali na aiki a wancan batu. Ba gaba ɗaya bayyana definition. Bari mu bincika shi a daki-daki. Zata da muke da wani jadawali na wani aiki (dauki amfani kwana). Shi yana da wani iyaka yawan maki, amma akwai wuraren da guda ɗaya kawai nufi yana da a kalla ko m. Ta hanyar irin wannan batu, za ka iya zana a mike layin, wanda zai zama perpendicular zuwa jadawali na aiki a wancan batu. Wannan line za a kira wani tangent. Misali mu gudanar da shi har zuwa mahada tare da axis sa. Saboda haka samu tsakanin tangent da axis sa da kwana za a ƙaddara da wanda aka samu. More musamman, da tangent na wannan kusurwa zai zama daidai da shi.

Bari mu magana kadan game da musamman lokuta da kuma Kalam Bari mu bincika lambobin.

lokuta na musamman

Kamar yadda muka ambata, Kalam na lambobin - wani wanda aka samu darajar a wani batu. A nan, misali, sama da aiki y = x ^2. The wanda aka samu daga x - lambobi, amma a general - wani aiki daidai da 2 * x. Idan muka bukatar yin lissafi da wanda aka samu, misali, a aya x ₀ = 1, mun samu y '(1) = 2 * 1 = 2. Yana da matukar sauki. An ban sha'awa hali ne wanda aka samu daga cikin hadaddun lambar. Don shiga cikin wani cikakken bayani game da abin da wani hadadden lambar, ba za mu. Isar da shi a ce wannan lambar wanda yana dauke da ake kira hasashen naúrar - da lambar wanda square daidai -1. A lissafi na wannan wanda aka samu shi ne kawai zai yiwu a karkashin wadannan yanayi:

1) Akwai dole ne farko domin m Kalam na real kuma hasashen sassa na y kuma X.

2) a kan yanayin da Cauchy-Riemann hade tare da daidaici m bayyana a farkon sakin layi.

Wani mai ban sha'awa harka, ko da yake ba kamar yadda wuya kamar yadda baya daya, shi ne mai wanda aka samu da wani mummunan lambar. A gaskiya ma, wani korau lambobin za a iya wakilta a matsayin mai kyau, ta tara da -1. To, da wanda aka samu da akai aiki daidai da akai yawaita da wanda aka samu daga cikin aikin.

Yana zai zama mai ban sha'awa su koyi game da muhimmancin Kalam a cikin su a rayuwarsu ta kullum, da kuma wannan ne yanzu da kuma tattauna da shi.

aikace-aikace

Kila kowannenmu akalla sau daya a rayuwa, kama kaina tunanin cewa ilmin lissafi ne mai wuya ya zama da amfani a gare shi. Kuma irin wannan rikitarwa abu a matsayin wanda aka samu tabbas yana da wani amfani. A gaskiya, da ilimin lissafi - muhimman hakkokin kimiyya, da kuma duk da 'ya'yan itatuwa tasowa, yafi kimiyyar lissafi, sunadarai, ilmin taurari har ma da tattalin arzikin kasar. Wanda aka samu ya zamo farkon ilmin lissafi analysis, wanda ya ba mu zarafin mu zana karshe daga jadawalai na ayyuka, kuma muka koya fassara da dokoki na halitta da kuma juya su su amfani saboda shi.

ƙarshe

Hakika, ba kowa da kowa zai iya zama da amfani ga wanda aka samu a hakikanin rai. Amma ilimin lissafi tasowa dabaru cewa lalle za bukatar. Ba don kome ba saboda lissafi ne da ake kira sarauniyar sciences: shi kunshi wani tushen fahimtar sauran fannoni na ilimi.