Babban lissafi Eyler Leonard: nasarori a ilmin lissafi, wasu ban sha'awa facts, a takaice dai biography

Leonard Euler masanin lissafi ne da likitancin Jamus, daya daga cikin mawallafin lissafi. Ba wai kawai ya ba da gudummawa ta hanyar kirkiro da lissafi, masana'antu da kuma ka'idodi ba, amma ya kuma samar da hanyoyin magance matsalolin da ake amfani da ita a tsarin nazarin kimiyya da amfani da ilimin lissafi a cikin aikin injiniya da kuma harkokin jama'a.

Euler (mathematician): taƙaitaccen labari

An haifi Leonard Euler a ranar 15 ga Afrilu, 1707. Shi ne ɗan fari Paulus Euler da Margaret Brucker. Mahaifin yana daga cikin 'yan fasaha masu daraja, kuma magabatan Margaret Brucker da dama ne masanan kimiyya. Paulus Euler a wancan lokacin ya kasance mai shan nasara a coci na St. Jacob. A matsayin likitan tauhidi, mahaifin Leonard yana sha'awar ilimin lissafi, kuma a cikin shekaru biyu na farko na karatun a jami'a ya halarci darussan sanannen Yakubu Bernoulli. Game da shekara daya da rabi bayan haihuwar dansa, iyalin suka koma Rien, wani yanki na Basel, inda Bulusus Euler ya zama fasto a cikin Ikilisiya. A can ya yi da aminci da aminci har ya zuwa ƙarshen kwanakinsa.

Iyali suna rayuwa a cikin matsala, musamman bayan haihuwar jariri na biyu, Anna Maria, a cikin 1708. Ma'aurata za su sami 'ya'ya biyu - Mary Magdalena da Johann Heinrich.

Darasi na farko na Leonard na ilmin lissafi sun karbi gida daga mahaifinsa. A lokacin da yake da shekaru takwas an aika shi zuwa makarantar Latin a Basel, inda ya zauna a gidan mahaifinta. Don rama wajan rashin ilimin makaranta a wannan lokacin, mahaifinsa ya hayar da wani mai koyar da kai tsaye, wani matashi mai suna Johannes Burkhardt, mai sha'awar ilimin ilmin lissafi.

A watan Oktoba 1720, lokacin da yake da shekaru 13, Leonard ya shiga Jami'ar Basel a Faculty of Philosophy (yawancin lokaci a wannan lokacin), inda ya halarci gabatarwa a cikin ilimin lissafi na Johann Bernoulli, ɗan ƙaramin Yakubu, wanda ya mutu a lokacin.

Matashi Euler ya fara yin karatu tare da irin wannan himma da ya jawo hankalin malamin nan da nan, wanda ya karfafa shi ya yi nazarin littattafan da suka fi rikitarwa na aikinsa har ma da aka ba su don taimakawa wajen karatu a ranar Asabar. A 1723, Leonard ya kammala karatunsa tare da digiri na digiri kuma karanta karatun jama'a a Latin, inda ya kwatanta tsarin Descartes tare da falsafancin falsafar Newton.

Bisa ga son iyayensa, ya shiga cikin ilimin tauhidin, amma ya fi yawancin lokaci zuwa lissafi. A ƙarshe, watakila, a yayin da Johann Bernoulli ya ɗauka, mahaifinsa ya dauki nauyin kaddarar dan Adam don yin kimiyya, ba aikin koyarwa ba.

A lokacin da yake da shekaru 19, Euler ya yi ƙoƙari ya yi gasa tare da manyan masana kimiyya a wannan lokacin, ya shiga cikin gasar don magance matsalolin Cibiyar Kimiyya ta Paris a kan mafi kyawun jeri na masarugin jirgin ruwa. A wannan lokacin, bai taba ganin jirgi a rayuwarsa ba, ya lashe lambar yabo ta farko, amma ya dauki matsayi na biyu. Bayan shekara guda, lokacin da aka samu wani wuri a Sashen Harkokin Jiki a Jami'ar Basel, Leonard, tare da goyon bayan jagoransa Johann Bernoulli, ya yanke shawarar yin gasa a wurin, amma ya ɓace tun yana da shekaru kuma ba shi da jerin littattafai mai ban sha'awa. A wata ma'ana, ya kasance da farin ciki, tun da yake ya iya karɓar gayyatar Cibiyar Kimiyya ta St. Petersburg, wadda Tsar Peter I ta kafa a shekarun da suka gabata, inda Euler ya sami filin da ya fi dacewa da shi ya ba shi damar ci gaba. Babban rawa a cikin wannan ya buga Bernoulli da 'ya'yansa maza biyu, Nicklaus II da Daniel I, waɗanda suke aiki a can.

St. Petersburg (1727-1741): Saurin kaiwa

Euler ya ci hunturu na 1726 a Basel, nazarin ilmin jiki da ilmin lissafi a shirye-shiryen aiwatar da ayyukan da ake bukata a makarantar. Lokacin da ya isa St Petersburg kuma ya fara aiki a matsayin mai gyara, ya zama dole ya zama dole ya bada kansa ga ilimin lissafi. Bugu da ƙari, an bukaci Euler ya shiga cikin gwaje-gwaje a cikin Cadet Corps kuma ya ba da shawara ga gwamnati kan al'amurran kimiyya da fasaha daban-daban.

Leonard sau da yawa ya saba da sababbin yanayin rayuwa a arewacin Turai. Ba kamar sauran 'yan} asashen waje na makarantar ba, sai ya fara fara koyon harshen Rasha da sauri ya fahimta, duka a cikin rubuce-rubucen da kuma maganganu. A wani lokaci ya zauna tare da Daniel Bernoulli kuma ya kasance abokai da Kirista Goldbach, sakataren sakandare na makarantar kimiyya, wanda aka sani a yau don matsalar da ba a warware shi ba, bisa ga wanda aka ƙidaya, tun daga farkon 4, za a iya wakilta shi a cikin jimla biyu. Babban rubutu tsakanin su shine muhimmin tushe a tarihin kimiyya a karni na sha takwas.

Leonard Euler, wanda nasarorinsa a lissafin lissafi ya ba shi duniya da dama kuma ya karu da matsayi, ya kasance a cikin shekaru mafi yawan ilimi.

A cikin Janairu 1734 ya auri Katarina Gzel, 'yar wani dan kasar Swiss wanda ya koya tare da Euler, sai suka koma gidansu. A cikin auren 13 an haife su, wanda, duk da haka, kawai biyar sun kai girma. Dan fari, Johann Albrecht, ya zama masanin lissafi, kuma daga baya ya taimaki mahaifinsa a aikinsa.

Euler bai kauce wa wahala ba. A shekarar 1735 sai ya fara rashin lafiya kuma ya kusan mutu. Don babbar taimako ga dukan mutane, ya warke, amma bayan shekaru uku ya sake ciwo. A wannan lokacin cutar ta sa masa ido na dama, wanda yake a bayyane yake a duk hotuna na masanin kimiyya tun lokacin.

Harkokin siyasa a Rasha, wanda ya zo bayan mutuwar Sarauniya Anne Ivanovna, tilasta Euler ya bar St. Petersburg. Bugu da ƙari, ya gayyaci sarki Frederick II na Prussian zuwa Berlin don taimakawa wajen kafa Cibiyar Ilimin Kimiyya a can.

A Yuni 1741, Leonard, tare da matarsa Katarina, dan shekaru shida Johann Albrecht da Karl mai shekaru daya, suka bar St. Petersburg don Berlin.

Aiki a Berlin (1741-1766)

Rundunar sojojin ta Silesia ta dakatar da shirin Friedrich II don kafa makarantar kimiyya. Kuma kawai a cikin 1746 an ƙarshe an kafa shi. Shugaban shi ne Pierre-Louis Moro de Maupertuis, kuma Euler ya ɗauki mukamin darekta na sashen lissafi. Amma kafin wannan bai zauna ba. Leonard ya rubuta game da abubuwa 20 da suka shafi kimiyya, da mahimman litattafai guda biyar kuma ya sanya fiye da 200 haruffa.

Duk da cewa Euler ya yi ayyuka da yawa - yana da alhakin kulawa da lambun gonar inabi, ya magance matsalolin ma'aikata da kuma kudi, ya kasance yana sayar da almanacs wanda ya zama tushen tushen karatun, ba tare da ambaci ayyukan fasaha da aikin injiniya ba, ba a shafi aikin lissafi ba.

Har ila yau, ba a shawo kan matsalar da aka yi ba, wanda ya bayyana a farkon shekarun 1750, wanda Maupertuis ya ce, wanda masanin kimiyyar Swiss da sabon malamin makarantar da aka zaɓa, Johann Samuel Koenig, ya yi masa magana game da yadda ya ambaci Leibniz a wasikar Yakubu Herman. Koenig na kusa da zargin Maupertuis na nuna rashin tausayi. Lokacin da aka tambaye shi ya gabatar da wasikar, ba zai iya yin hakan ba, kuma an umurci Euler ya bincika al'amarin. Da ciwon ba tausayi ga falsafar Leibniz, ya goya tare da shugaban kasar da kuma zargin da König na zamba. Wannan matsala ta zo ne a lokacin da Voltaire, wanda ya dauki gefen Koenig, ya rubuta wani sakonni mai laushi, ya yi ba'a da Maupertuis kuma bai daina Euler. Shugaban kasa ya damu ƙwarai da cewa ya bar Berlin nan da nan, kuma Euler ya gudanar da kasuwanci, da gaske ya shiga makarantar.

Iyalan masanin kimiyya

Leonard ya zama mai arziki da ya saya wani gida a Charlottenburg, wani ɓangare na yammacin Berlin, wanda ya isa ya ba da kwanciyar hankali ga mahaifiyarsa, wanda ya kawo Berlin zuwa 1750, 'yar uwarsa da dukan' ya'yansa.

A 1754, an haifi dansa Johann Albrecht a kan shawarwarin Maupertuis a shekara 20, kuma ya zama memba a Jami'ar Berlin. A shekara ta 1762, aikinsa a kan tashe-tashen hankulan da aka samu a cikin makarantar Petersburg, wanda ya raba da Alexis Claude Claire. Ɗan na biyu na Euler, Karl, ya yi nazarin magani a Halle, kuma na uku, Christophe, ya zama jami'in. Yarinyar Charlotte ta yi auren dan kasar Holland, da kuma 'yar'uwarsa Helena a shekara ta 1777 - ga wani jami'in Rasha.

Abokan Sarki

Harkokin masana kimiyya tare da Frederick II ba sauki. Wannan shi ne jera matukar a kan wani gagarumin bambanci a cikin sirri da kuma falsafa leanings Frederick - mai girman kai, kai m, m kuma witty conversationalist, a sympathizer na Faransa haske. Mathematician Euler wani hali ne mai laushi, maras dacewa, ƙasa da ƙasa da kuma Protestant masu ibada. Wani, watakila mafi mahimmanci, dalilin da ya sa Leonard ya zagi da cewa ba a taba ba shi mukamin shugaban Kwalejin Berlin ba. Wannan fushi ne kawai ya karu bayan da Maupertuis ya tashi da kuma kokarin Euler don ci gaba da kula da hukumar a yayin da Friedrich ke kokarin neman shugabancin shugaban kasar Jean Léron D'Alembert. Wannan karshen ya zo Berlin ne, amma don sanar da sarkin saɓin kuma ya ba Leonard shawara. Friedrich ba wai kawai ya manta da shawarar D'Alembert ba, amma ya nuna kansa a matsayin shugaban makarantar. Wannan, tare da sauran kasawar da aka yi wa sarki, ya haifar da gaskiyar cewa tarihin lissafin lissafi Euler ya sake zama mai mahimmanci.

A shekara ta 1766, duk da matsalolin sarkin, sai ya bar Berlin. Leonard ya karbi gayyatar Wakilin Catherine Catherine II ya koma St. Petersburg, inda ya sake ganawa da juna.

Again St. Petersburg (1766-1783)

An girmama shi a makarantar kimiyya kuma ta yi masa sujada a Kotun Katarina, babban masanin lissafin Euler yana da matsayi mai mahimmanci kuma yana jin dadin rinjayar, wanda ya ƙi yarda da shi a Berlin. A gaskiya ma, ya taka rawar jagorancin ruhaniya, idan ba shugaban makarantar ba. Abin baƙin ciki, duk da haka, tare da lafiyarsa, ba duk abin da ya ci gaba sosai ba. Cutar da ido na hagu, wanda ya fara damuwa da shi a Berlin, ya zama mafi tsanani, kuma a 1771 Euler ya yanke shawarar aiki. Sakamakonsa shi ne kafa wani ƙananan ƙwayar cuta, wanda kusan kusan ya lalace.

Daga baya a wannan shekara, a lokacin babban wuta a St. Petersburg, gidansa na katako ya fadi, kuma kusan makafi Euler ya hana ya ƙona cikin rai kawai saboda godiya ga Bitrus Grimm, masanin Basel. Don saukaka yanayin masifa, Mai Girma ya ba da kuɗi domin gina sabon gidan.

Har ila yau, Euler ya sake bugawa mai tsanani a 1773, lokacin da matarsa ta mutu. Shekaru uku bayan haka, don kada ya dogara ga 'ya'yansa, sai ya sake yin aure a karo na biyu a' yar'uwarsa Salome-Avigeye Gzel (1723-1794).

Duk da wadannan abubuwan da suka faru, malamin likitancin L. Euler ya kasance a cikin kimiyya. Lalle ne, kusan rabin aikinsa aka buga ko an haife su a St. Petersburg. Daga cikin su, biyu daga cikin "littattafai masu sayar da kaya" sune "Lissafin zuwa Gidan Jumhuriyar Jamus" da "Algebra." A hakika, ba zai iya yin hakan ba tare da sakatare mai kyau da kuma taimakon fasahar da Nicklaus Fuss ya ba shi ba, tare da wasu, wasu daga cikin wasu, wasu 'yan jarida daga Basel da kuma mijinta na' yar Euler. Ɗansa Johann Albrecht kuma ya shiga cikin wannan tsari. Har ila yau, mawallafin ya kasance wani abu ne, wanda ya zama babban jami'in harkokin kimiyya, inda masanin kimiyya, a matsayin mafi tsohuwar mamba, ya kasance shugaban} asa.

Mutuwa

Babban lissafi Leonhard Euler rasu a bugun jini 18 Satumba 1783 yayin da wasa tare da jikansa. A ranar mutuwar ta biyu manyan slates aka samu dabarbari cewa bayyana a balan-balan jirgin, cikakken Yuni 5, 1783 a birnin Paris, da Montgolfier 'yan'uwa. An kirkiro ra'ayin kuma an shirya shi ne ta dan Johann. Wannan shi ne labarin karshe na masanin kimiyya, wanda aka buga a cikin 1784th girma na Memoires. Leonard Euler da taimakonsa zuwa ilmin lissafi sun kasance masu girma da yawa har yanzu an cigaba da kwarara abubuwan da ke jiran jigilar su a cikin littattafan kimiyya shekaru 50 bayan mutuwar masanin kimiyya.

Ayyukan kimiyya a Basel

A lokacin gajeren lokaci na Basel, an ba da gudunmawa ga lissafin lissafin lissafin lissafin lissafin lissafin lissafin lissafin lissafin lissafin lissafin lissafin lissafi, da kuma aiki na kyautar Prize a Paris Academy. Amma babban aiki a wannan mataki shi ne Dissertatio Physica de sono, ya gabatar da goyon baya ga gabatarwarsa ga Sashen Harkokin Kwayoyin Jiki a Jami'ar Basel, game da yanayin da rarraba sauti, musamman, game da saurin sauti da tsarata ta kayan kida.

Taron farko na St. Petersburg

Duk da kiwon lafiya da matsaloli samu ta hanyar Euler, na cigaba a ilmin lissafi, masanin kimiyyar ba zai iya amma sa mamaki. A wannan lokacin, baya ga manyan ayyuka a masana'antu, ka'idar kiɗa, da masaukin jirgi, ya rubuta rubutun 70 a kan batutuwa daban-daban, daga nazarin ilmin lissafi da kuma ka'idodin lambobi zuwa wasu matsalolin da suka shafi ilimin lissafi, injiniyoyi da kuma astronomy.

Ma'anonin "Mechanics" guda biyu sune farkon mafitaccen nazari na cikakken nazarin duk nau'in masanan, ciki har da masu kwakwalwa masu tsabta, masu sassaucin ra'ayi da masu ruba, da magunguna da magunguna na sama.

Kamar yadda ake iya gani daga litattafai na Euler, ko da a Basel, ya yi tunani mai yawa game da kiɗa da kuma kundin kiɗa kuma ya shirya ya rubuta littafi. Wadannan tsare-tsaren sun tsufa a St. Petersburg kuma sun ba da aikin aikin Tentamen, wanda aka buga a 1739. Wannan aikin ya fara ne tare da tattaunawar yanayin sauti kamar yadda ake nunawa a cikin iska, ciki har da fadadawa, da ilimin kimiyya na hangen nesa da kuma ƙarfin sauti ta hanyar kirtani da kayan murya.

Babban aikin shine ka'idar jin dadi, ta hanyar kiɗa, wadda Euler ya tsara ta hanyar sanya nauyin sauti, jimla ko jerin su zuwa ƙididdigar lissafi, nauyin digiri wanda ya zama "ƙaunar" wani aikin fasaha da aka ba da shi: ƙananan digiri, mafi girma da jin dadi. Anyi aikin ne a cikin yanayin da masanan ya ƙaunaci diatonic ƙauna, amma har da ka'idar lissafin ilmin lissafi (duka d ¯ a da zamani) aka ba. Euler ba shine kadai wanda yayi ƙoƙari ya kunna kiɗa a kimiyya daidai ba: Descartes da Mersenne sunyi irin wannan a gabansa, kamar D'Alembert da sauran mutane bayansa.

Sakamakon digiri biyu na Scientia Navalis shi ne mataki na biyu na ci gaba da masana'antu. Littafin ya kwatanta ka'idojin hydrostatics kuma ya haɓaka ka'idar ma'auni da kuma vibrations na jikin jiki uku da aka cika a cikin ruwa. Ayyukan suna dauke da ginshiƙan masanan nau'ikan kwayoyin halitta, waɗanda suka bayyana a baya a littafin Theoria Motus corporum solidorum seu rigidorum, na uku mafi girma mahimmanci a kan masanan. A jujjuya na biyu, ana amfani da ka'idar akan jiragen ruwa, ginin jirgi da kewayawa.

Abin mamaki shine, Leonard Euler, wanda nasarorinsa a cikin ilmin lissafi sun kasance masu ban sha'awa a wannan lokacin, suna da lokacin da ƙarfin zuciya don rubuta ayyukan aiki na 300 a kan jinsin farko don amfani a gymnasiums na St. Petersburg. Yaya galibin sune 'ya'yan da masanin kimiyya suka koya!

Berlin aiki

Baya ga abubuwa 280, da dama daga cikinsu sune mahimmanci, a wannan lokacin masanin lissafi Leonard Euler ya samar da wasu ƙididdigar kimiyya na zamani.

Matsalar brachistochrone - binciken ne game da hanyar da maki ke motsawa a ƙarƙashin aiki na nauyi daga wani aya a cikin jirgin sama na tsaye zuwa ɗayan a cikin mafi guntu lokaci - alamar misali ne na matsalar da Johann Bernoulli ya kafa don neman aiki (ko ƙoƙari) wanda ke ingantaccen maganganun, Wanne ya dogara da wannan aikin. A 1744, sa'an nan kuma a 1766, Euler yayi yawa akan wannan matsala, yana samar da sabon sashe na ilmin lissafi - "lissafi na bambancin".

Ƙididdigar ƙarami guda biyu, game da burbushin sararin samaniya da haɗe-haɗe da kuma kayan fasaha, sun bayyana kusan 1744 da 1746. Wannan ƙarshen yana da sha'awar tarihi, tun lokacin da ya fara tattaunawa game da ƙwayoyin Newtonian da kuma ka'idar kalaman Euler.

A biyayya ga m, Sarki Frederick II, Leonard ya juyar da muhimmanci a kan aikin ballistics Banasare Benjamin Robins, ko da yake ya riƙa soki da "makanikai" a 1736 Ya kara da cewa, duk da haka, saboda haka da yawa comments, Bayani bayanin kula da gyare-gyare, a sakamakon littafin "harbi" (1745) da kundinta ne 5 sau mafi girma fiye da asali.

Biyu-girma "Gabatarwa zuwa infinitesimal analysis" (1748), lissafi Euler sakawa analysis matsayin mai zaman kanta horo, ya takaita da yawa binciken a fagen iyaka jerin, iyaka kayayyakin da ci gaba kasarun adadi. Yana tasowa wani haske aiki na real da hadaddun dabi'u da kuma jaddada da muhimman hakkokin rawa a cikin bincike na yawan e, karuwa da sauri, kuma logarithmic ayyuka. Na biyu girma da aka sadaukar da hikimar tantance lissafi: ka'idar algebraic masu lankwasa da kuma saman.

"Bambanci ilimin lissafi" kuma kunshi sassa biyu, na farko na abin da aka kishin lissafi na da bambance-bambance da kuma differentials, da kuma na biyu - da ka'idar ikon jerin summation dabara da tare da babban yawan misalai. A nan, ba zato ba tsammani, na dauke da farko buga Fourier jerin.

The uku-girma "na game ilimin lissafi" lissafi Euler la'akari quadrature (m. E. M iteration) na farko ayyuka da kuma fasahar don a kawo su mikakke bambanci lissafai, wani cikakken bayanin da ka'idar mikakke bambanci lissafai na biyu domin.

A ko'ina cikin shekaru a Berlin, da kuma daga baya Leonard karatu geometrical kimiyyan gani da hasken wuta. Kasidunsu da littattafai a kan batun, ciki har da monumental uku-girma "Dioptrics" amounted zuwa bakwai kundin na Opera Omnia. A tsakiyar jigo na wannan aikin shi ne don inganta Tantancewar kida kamar nesa da microscopes, da yadda za a warware chromatic da kuma siffar zobe aberration ta wani hadadden tsarin da ruwan tabarau da kuma cika ruwaye.

Euler (lissafi): Interesting Facts na biyu St. Petersburg lokaci

A da mafi m lokaci, a lokacin wadda masana kimiyya ta buga fiye da 400 takardunku a kan batutuwa riga aka ambata, kazalika da lissafi, yiwuwar samun ka'idar da statistics, Taswirar, kuma ko da fensho kudi ga mata gwauraye da kuma aikin noma. Daga gare su, za a iya raba uku treatises a kan aljabara, ka'idar da Moon da kuma sojan ruwa kimiyya, kazalika a kan ka'idar lambobi, halitta falsafa da kuma dioptrics.

Ga zo da wani daga cikin "bestseller" - "aljabara." Sunan lissafi Euler ado wannan 500-shafi aikin, wanda aka rubuta tare da manufar da horo ne domin ya koyar da wata cikakkar mafari. Ya shibtarsu da littafin da matasa almajiri, wanda ya fisshe tare da shi daga Berlin, da kuma lokacin da aikin da aka gama, ya gane duk kan kuma ya iya sosai sauƙi shirya algebraic matsaloli shirya kai zuwa gare shi.

"Sannan mahanga ta biyu, daga jirgi" da aka ma tsara don mutanen da suke da wani ilmi game da lissafi, wato - da matuƙan. Ba abin mamaki ba cewa aikin ya kasance mai nasara godiya ga m didactic basira da marubucin. Ministan Navy da kuma Faransa Finance Anne-Robert Turgot samarwa ga sarki Louis XVI ya bukaci dukkan dalibai na marine da kuma manyan bindigogi makarantu don nazarin Euler rubutun. Yana da matukar ila cewa daya daga cikin dalibai ya juya ga Napoleon Bonaparte. Sarkin ma biya 1,000 rubles ilimin lissafi ga gata na republishing da aikin, da kuma Empress Catherine II, ba so ba a wurin sarki, ya ninka yawan, da kuma babban lissafi Leonhard Euler bugu da žari samu 2000 rubles!