Ma'anar haɗin kai
Haɗin kai aiki ne na lissafi da ake amfani da shi a cikin lissafi, kuma shi ne tsarin bambance-bambance. Ana amfani da haɗin kai don nemo ɗimbin amfani masu yawa, kamar yankuna, kundin, ƙaura, da sauransu. Alamar haɗin kai tana wakilta ta alamar ∫, wadda ba za ta iya rarrabawa ba. Haɗin kai ta hanyar musanya hanya ce mai amfani don canza sifar haɗin gwiwa zuwa nau'i na sananne, yana sauƙaƙa samunsa. Haɗin kai shine ƙaƙƙarfan ƙididdigewa da ake iya rarrabawa, ra'ayi na lissafi wanda ke ba mu damar nemo yanki, ƙara, taro, ko kowane saitin abubuwa marasa iyaka.
Menene nau'ikan haɗin kai?
Akwai nau'ikan haɗin kai daban-daban a cikin ilimin lissafi. Waɗannan nau'ikan sun haɗa da haɗin kai mara iyaka da haɗin kai mai iyaka. Haɗin da ba shi da iyaka wani yanki ne mara ganuwa na aiki lokacin da babu takamaiman iyaka ga abin da aka haɗa, ma'ana ana iya ƙididdige shi ga kowace ƙima na ma'auni mai zaman kansa. Dangane da haɗin kai mai iyaka, tsari ne wanda ke ƙididdige yanki a ƙarƙashin wani yanki kuma sama da axis x a cikin takamaiman kewayon. Ana amfani da waɗannan nau'o'in haɗin kai daban-daban a fannoni daban-daban kamar lissafi, kimiyyar lissafi, tattalin arziki, injiniyanci, da dai sauransu, inda kwararru ke amfani da su don magance matsaloli, nazarin bayanai, da amfani da ƙira masu rikitarwa.
Menene halayen haɗin kai?
Abubuwan haɗin kai sune dokoki da ra'ayoyi waɗanda suka shafi tsarin haɗin kai a cikin lissafi. Kaddarorin haɗin kai suna taimakawa sauƙaƙe ayyukan lissafi kuma suna ba da hanyoyi don ƙididdige ƙimar da ake buƙata cikin sauƙi. Akwai mahimman halaye da yawa na haɗin kai, gami da:
- Oda dukiya: Wannan yana nufin cewa iyakokin haɗin kai za a iya ba da oda kuma ana iya ba da umarnin iyakokin haɗin kai waɗanda ke da ƙimar iri ɗaya. A wasu kalmomi, ana iya maye gurbin sharuɗɗan haɗin kai a cikin ma'auni da wasu sharuɗɗa masu daraja ɗaya, ba tare da canza sakamakon ba.
- Jima'i da bambancin dukiya: Ana iya canza tsarin haɗin kai zuwa jimla ko bambancin ayyuka da yawa. Ta wannan hanyar, ana iya sauƙaƙe ayyukan kuma yana da sauƙin ƙididdige ƙimar da ake buƙata.
- Inverse Property: Idan samfurin haɗin kai tsakanin ƙayyadaddun tazara guda biyu yayi daidai da mummunan samfurin tsakanin tazarar jujjuyawar biyu, ana iya amfani da wannan kadarar don sauƙaƙe ayyuka.
- Abubuwan da ke da alaƙa na haɗin kai: yana nuna cewa ana iya zaɓar abubuwan gama gari a cikin ayyuka don sauƙaƙe tsarin haɗin kai da sauƙaƙe lissafin sakamakon.
Menene tushen haɗin kai?
Ka'idojin haɗin kai muhimmin ɓangare ne na lissafi kuma suna wakiltar kayan aiki na asali a cikin nazarin haɗin kai. Yana taimakawa wajen fahimtar dabaru da aikace-aikace da yawa a cikin wannan kimiyyar lissafi. Waɗannan ka'idoji sun shafi haɗin kai da iko, bambance-bambancen ayyuka, da dokokin bambance-bambance da haɗin kai.
Ɗaya daga cikin tushen haɗin kai shine cewa shi ne tsarin bambance-bambance. Yayin da bambance-bambance ya shafi sanin ƙimar canjin aiki dangane da canjin sa, haɗin kai yana mai da hankali kan ƙididdige yankin da ke ƙarƙashin lanƙwan aikin tsakanin haɗin gwiwarsa. Hakazalika, ƙididdiga na asali bincike ne akan ma'anar iyakoki da ayyuka.
Bugu da ƙari, ƙa'idodin haɗin kai na asali sun faɗi ƙarƙashin wasu ra'ayoyi kamar ci gaba da ma'auni. Ta hanyar ci gaba da fassarori, ɗalibai za su iya fahimtar alaƙa iri-iri tsakanin ayyuka da dokokin haɗin kai, gami da ƙa'idar haɗakarwa da ƙa'idar daidaitawa don ayyuka masu juzu'i.
Gabaɗaya, ana iya cewa nazarin ƙa'idodin haɗin kai na asali yana ba da gudummawa ga zurfin fahimtar ilimin lissafi kuma yana ba da damar yin amfani da haɗin kai a fannoni daban-daban kamar injiniya, kimiyyar lissafi da kimiyyar kwamfuta. Don haka, ƙware waɗannan mahimman abubuwan yana da mahimmanci ga duk mai sha'awar ilimin lissafi.
Yaya ake lissafin yanki ta hanyar haɗin kai?
Ana iya ƙididdige yanki ta hanyar haɗawa cikin lissafi. An ayyana haɗin kai azaman haɗaɗɗiyar rarrabuwar ƙima mai ƙima kamar yanki, girma, taro, da kowane adadin ƙananan abubuwa. Ana kallon haɗin kai azaman kayan aiki don ƙididdige yankin da aka ɗaure da lanƙwasa. A cikin wannan mahallin, ana amfani da haɗin kai don nemo yanki na yanki tsakanin lanƙwasa biyu ko fiye. Wajibi ne don samar da ma'auni na aiki da kuma nemo wuraren haɗin gwiwa tsakanin su. Ƙididdigar wurare ta hanyar haɗin kai an bayyana shi azaman abin da ke cikin babban lanƙwasa akan madaidaicin kwancen da aka cire daga gare ta. Hakanan ana iya amfani da haɗin kai don ƙididdige wurare a cikin ƙididdiga ta hanyar musanya dabi'u a cikin haɗin kai don nemo wuraren haɗin kai tsakanin masu lanƙwasa.
Shin sarari zai iya zama mara kyau?
Mutane da yawa suna mamaki ko sarari na iya zama mara kyau. Ko da yake mun san cewa yanki tabbataccen adadi ne wanda ke nuna sararin da wani abu ya mamaye, akwai lokuta inda cikakkiyar ƙimar yanki ta bayyana a matsayin ƙima mara kyau a wasu lokuta na tabbataccen haɗin kai.
Lokacin ƙididdige ƙayyadaddun abin da ke cikin lanƙwasa, an fi mayar da hankali kan yanki tsakanin lanƙwasa da axis x. A wasu lokuta, wannan yanki na iya zama ƙasa da axis x, ma'ana cikakkiyar ƙimar yankin zata zama mara kyau.
Sabili da haka, ana sanya alamar mara kyau a gaban haɗin kai don jaddada cewa yankin ba zai iya zama mara kyau ba. Lokacin ƙididdige ƙayyadaddun mahimmanci na waɗannan lokuta, ana amfani da cikakkiyar ƙimar yankin don hana samun ƙimar mara kyau, ta hanyar watsi da alamar mara kyau.
Ya kamata kuma mu ambaci cewa haɗin kai hanya ɗaya ce ta lissafin yanki, kuma idan ya nuna akan ma'aunin lissafi yanki da bai kai sifili ba, ana fassara wannan ta ma'anar cewa wuraren da za a lissafta suna kwance a ƙasa da axis x don haka suna ƙasa da sifili. cikakkiyar darajar.
A ƙarshe, zamu iya cewa cikakkiyar ƙimar yankin ba ta da kyau, amma ainihin ƙimar ƙayyadaddun ƙayyadaddun kayan aiki na iya zama mara kyau idan akwai wani yanki a ƙarƙashin x-axis. Wannan ƙimar ta gamsar da manufar ƙididdige yanki ba tare da yankin da kansa ya kasance mara kyau ba.
