Qhov zoo mathematician Eyler Leonard: tau nyob rau hauv kev kawm txog zauv, ib co nthuav cov lus tseeb, ib tug nyuag Phau ntawv sau

Leonhard Euler - Swiss mathematician thiab physicist, ib tug ntawm cov founders ntawm ntshiab kev kawm zauv. Nws tsuas tsis ua ib tug siv thiab formative pab rau geometry, calculus, mechanics thiab cov kev tshawb xav ntawm tus xov tooj, tab sis kuj tsim txoj kev daws cov teeb meem ntawm observational astronomy thiab thov lej nyob rau hauv engineering thiab pej xeem tej hauj lwm.

Euler (mathematician): ib tug luv luv biography

Leonhard Euler yug Plaub Hlis Ntuj 15, 1707 Nws yog tus thawj-yug Paulus Euler thiab Margaret Brooker. Cov txiv los ntawm ib tug zoo ntawm craftsmen, thiab cov pog koob yawg koob ntawm Margaret Brooker muaj ib tug xov tooj ntawm zoo-paub zaum. Paulus Euler tau txais kev pab nyob rau ntawm lub sij hawm vicar nyob rau hauv lub tsev teev ntuj ntawm St. Jakob. Raws li ib tug theologian, Leonard tus txiv yog xav nyob rau hauv kev kawm txog zauv, thiab nyob rau hauv thawj ob lub xyoos ntawm txoj kev tshawb ntawm lub tsev kawm ntawv mus kawm cov hoob uas kawm ntawm tus naas ej Yakoba Bernulli. Tom qab hais txog ib lub xyoo thiab ib tug ib nrab tom qab yug me nyuam ntawm lawv tus tub, tsev neeg tsiv mus rau Riehen, Basel suburb qhov twg Paulus Euler los ua tus xibhwb ntawm lub zos parish. Muaj nws thiab rau siab ntso ua tau txais kev pab kom txog thaum nws tuag.

Cov tsev neeg nyob hauv cramped tej yam kev mob, tshwj xeeb tshaj yog tom qab yug tus me nyuam ntawm nws ob tus me nyuam, Anna-Maria, nyob rau hauv 1708. Qhov ob peb yuav tsum muaj ob tug me nyuam - Maria Magdalena thiab Johann Heinrich.

Cov zaj lus qhia thib nyob rau hauv kev kawm txog zauv, Leonard tau txais nyob rau hauv tsev los ntawm nws tus txiv. Nyob ib ncig ntawm lub hnub nyoog ntawm yim nws twb muab xa mus rau lub Latin lub tsev kawm ntawv nyob rau hauv Basel, qhov twg nws nyob rau hauv lub tsev ntawm nws niam pog. Pab kom txawm peem rau cov neeg pluag zoo ntawm lub tsev kawm ntawv txoj kev kawm ntawv nyob rau ntawm lub sij hawm, kuv txiv ntiav ib tug private qhia, ib tug hluas theologian npe Johannes Burckhardt, ib tug passionate lover ntawm kev kawm txog zauv.

Nyob rau hauv Lub kaum hli ntuj 1720 thaum lub hnub nyoog ntawm 13 xyoo, Leonard nkag mus hauv lub tsev kawm ntawv ntawm Basel ntawm cov kws qhia ntawv ntawm Philosophy (ib qho tshwm sim thaum lub sij hawm), qhov uas nws tau mus kawm lub introductory hoob kawm nyob rau hauv elementary lej Ioganna Bernulli, tus yau tij laug ntawm tus tuag thaum lub sij hawm ntawm Yakhauj.

Hluas Euler li mob siab coj li nws cov kev tshawb fawb, uas tsis ntev attracted tus mloog ntawm tus xib fwb, uas pab txhawb nws mus kawm ntawv ntau phau ntawv ntawm nws tus kheej, thiab txawm muaj los pab nyob rau hauv lawv cov kev tshawb fawb nyob rau hauv hnub Saturday. Nyob rau hauv 1723, Leonard ua tiav nws txoj kev kawm ntawv nrog ib tug master degree thiab muab ib tug pej xeem qhuab qhia nyob rau hauv Latin, nyob rau hauv uas Descartes piv rau system nrog lub ntuj philosophy ntawm Newton.

Tom qab xav li cas ntawm nws niam nws txiv, nws cuv npe kawm nyob rau Theological kws qhia ntawv, siab ntso, txawm li cas los, feem ntau ntawm cov kev kawm txog zauv ntawm lub sij hawm. Nws thiaj li, tej zaum nyob rau lub insistence ntawm Ioganna Bernulli txiv nws coj rau pom zoo nws tus tub mus ua scientific lub hom phiaj, tsis yog ib tug Theological hauj lwm.

Nyob rau hauv 19 xyoo, lub mathematician Euler dared rau lwv nrog rau sab saum toj zaum ntawm lub sij hawm, noj ib feem nyob rau hauv cov kev sib tw rau hauv kev daws ntawm lub Paris Academy ntawm Sciences rau lub pom kev tso kawm ntawm lub nkoj Masts. Nyob rau ntawm lub taw tes nws yeej tsis nyob rau hauv kuv lub neej pom lub ships, lub nqi zog yog tsis yeej, tab sis yeej ib prestigious ob qhov chaw. Nyob rau hauv ib lub xyoo thaum muaj ib tug tsis txaus rau ntawm lub Department of Physics nyob rau University of Basel, Leonard, nrog kev pab los ntawm nws saib Ioganna Bernulli, nws txiav txim siab los sib ntaus sib tua rau ib qho chaw, tab sis poob vim hais tias ntawm lawv cov muaj hnub nyoog thiab tsis muaj ib tug impressive daim ntawv teev cov ntaub ntawv. Nyob rau hauv ib nws yog muaj hmoo vim hais tias nws muaj peev xwm los txais lub caw ntawm lub St. Petersburg Academy ntawm Sciences, nrhiav tau ib tug ob peb xyoos ua ntej lawm los Tsar Peter kuv, qhov twg lub Euler pom ib tug ntau pheej teb, uas ua rau nws los tsim rau cov hom phiaj zoo. Lub ntsiab luag hauj lwm yog ua si los ntawm Bernoulli thiab nws ob tug tub, Daniel Nicklaus II thiab kuv, leej twg muaj kev koom ua hauj lwm muaj.

St. Petersburg (1727-1741): ib tug meteoric sawv

Euler siv lub caij ntuj no ntawm 1726 nyob rau hauv Basel, kawm lub cev thiab tej hlab ntshav nyob rau hauv kev npaj rau lub tua ntawm lawv yuav tsum num ua nyob hauv lub academy. Thaum nws tuaj txog nyob rau hauv St. Petersburg thiab ua hauj lwm ib tug associate, nws tau los ua khees tias nws yuav tsum mob siab rau nws tus kheej rau zauv sciences. Nyob rau hauv tas li ntawd, los ntawm Euler twb yuav tsum tau mus koom nyob rau hauv qhov kev txiav txim-xeem nyob rau hauv lub Cadet Corps, thiab mus qhia rau tsoom fwv nyob rau hauv ntau yam scientific thiab cov kev teeb meem.

Leonard yooj yim nruj heev heev rau tshiab hnyav tej yam kev mob ntawm lub neej nyob rau hauv sab qaum teb ntawm teb chaws Europe. Tsis zoo li ntau lwm yam txawv teb chaws mej zeej ntawm lub academy, nws tam sim ntawd pib mus kawm Lavxias teb sab lus thiab mastered nws sai sai thiab nyob rau hauv daim ntawv thiab lub qhov ncauj ntaub ntawv. Rau ib lub sij hawm nws nyob nrog Daniel Bernoulli thiab yog cov phooj ywg nrog Christian Goldbach, Cob phum Secretary ntawm lub Academy, niaj hnub no lub npe hu rau nws tseem tsis solved qhov teeb meem, raws li uas tej txawm tooj ntawm 4, yuav sawv cev los ntawm lub sum ntawm ob primes. Cov uas nws kim heev xov xwm ntawm lawv yog ib qho tseem ceeb qhov twg los rau hauv lub keeb kwm ntawm science nyob rau hauv lub XVIII caug xyoo.

Leonhard Euler, kev kawm nyob rau hauv kev kawm txog zauv uas instantly coj nws thoob ntiaj teb lub koob meej thiab tsa nws raws li txoj cai, muaj nyob rau hauv lub Academy ntawm lawv feem ntau tsim xyoo.

Nyob rau hauv Lub ib hlis ntuj 1734, nws yuav tau Katarine Gzel, tus ntxhais ntawm lub Swiss artist, uas qhia nrog Euler, thiab lawv tsiv mus rau hauv lawv lub tsev. Cov sib yuav tuaj mus rau lub teeb 13 cov me nyuam, uas, li cas los xij, tsuas yog tsib mus txog adulthood. Thawj, Johann Albrecht, kuj los ua ib tug mathematician, thiab tom qab ntawd pab tau nws tus txiv nyob rau hauv nws cov hauj lwm.

Euler twb tsis spared raug kev txom nyem. Nyob rau hauv 1735, nws tau mob heev, yuav luag tuag. Rau cov poj nyem ntawm tag nrho cov, nws zoo tu qab tso, tab sis tom qab peb xyoos rov qab mob. Thaum lub sij hawm no, tus kab mob tau ua rau nws txoj kev qhov muag, uas yog kom meej meej pom nyob rau tag nrho cov portraits zaum los ntawm hais tias lub sij hawm.

Nom tswv tsis khov nyob rau hauv Russia, uas tshwm sim tom qab kev tuag ntawm poj huab tais Anna Ivanovna, Euler yuam kom khiav tawm St. Petersburg. Tshwj xeeb tshaj yog txij thaum nws muaj ib qho kev caw los ntawm lub Prussian King Friedrich II tuaj rau Berlin thiab pab tsim lub Academy ntawm Sciences muaj.

Nyob rau hauv Lub rau hli ntuj 1741, Leonard thiab nws tus poj niam Katarina, 6-xyoo-laus Johann Albrecht thiab ib xyoos-laus Carl tsav tsheb los ntawm St. Petersburg rau Berlin.

Cov hauj lwm nyob rau hauv Berlin (1741-1766)

Cov tub rog phiaj los nqis tes nyob rau hauv Silesia Frederick II tau muab ncua kev pab them nqi rau lub tsev lag luam ntawm lub academy. Thiab xwb nyob rau hauv 1746 nws raug thaum kawg tsim. Nws los ua tus thawj tswj hwm Pierre-Lui Moro de Maupertuis thiab Euler raug tsa thawj coj ntawm lub Mathematics Department. Tab sis ua ntej ntawd, nws tsis nyob twj ywm kaw. Leonard sau txog 20 scientific cov khoom, 5 loj treatises thiab ua ntau tshaj 200 tsiaj ntawv.

Txawm tias muaj tseeb hais tias Euler ua ntau ntau yam hauj lwm - lub luag hauj lwm rau lub observatory thiab cov botanical vaj, kom daws tau qhov cov neeg thiab nyiaj txiag teeb meem muab kev koom tes nyob rau hauv lub qhov muag ntawm almanacs, constituting lub ntsiab qhov chaw ntawm cov nyiaj khwv tau ntawm lub Academy, tsis hais qhov ntau hauj thiab engineering tej yaam num, nws xyuam xim ua tau zoo yog tsis cuam tshuam.

Tsis tas li ntawd, nws tsis yog ib yam nkaus thiab distracted los ntawm scandal ntawm lub primacy ntawm lub foundations ntawm cov hauv paus ntsiab lus ntawm tsawg kawg yog txiav txim, uas tsoo tawm nyob rau hauv thaum ntxov 1750s, thov los ntawm Maupertuis uas sib tw lub Swiss paub txog thiab tshiab khiv academician Johann Xamuyee Koenig, tham txog nws mention ntawm Leibniz sau ntawv mus rau mathematician Yakhauj Hermann. Koenig yog nyob ze rau Maupertuis nqi ntawm plagiarism. Thaum nws twb nug los ua tus tsab ntawv, nws yuav tsis tau ua nws, thiab Euler twb muab mus soj ntsuam cov ntaub ntawv. Muaj tsis muaj pab koj tu siab rau lub philosophy ntawm Leibniz, nws tog nrog tus thawj tswj hwm thiab accusing König ntawm kev dag. Lub ib kub npau npau taw tes twb mus txog thaum Voltaire, uas coj lub sab ntawm Koenig sau disparaging satire, lampooned Maupertuis thiab Euler spared. Cov thawj tswj hwm yog li ntawd chim hais tias nws tshuav Berlin sai, Euler thiab tau mus rau, de facto taws lub academy.

tsev neeg paub txog

Leonard ua li muaj myiaj hais tias nws tau muas cov qub txeeg qub tes nyob rau hauv Charlottenburg, Berlin lub thaj suburbs, loj txaus los xyuas kom meej ib tug xis nyob nws niam, uas tau coj tuaj rau Berlin nyob rau hauv 1750, ib nrab-muam thiab tag nrho nws cov me nyuam.

Nyob rau hauv 1754, nws thawj-yug Johann Albrecht rau kev pom zoo ntawm Maupertuis thaum lub hnub nyoog ntawm 20 xyoo thiab tau raug xaiv los mus rau lub Berlin Academy. Nyob rau hauv 1762, nws ua hauj lwm nyob rau hauv perturbations ntawm lub orbits ntawm comets rub ntawm lub ntiaj teb twb muab tsub lub nqi zog ntawm lub St. Petersburg Academy, uas nws muab qhia nrog Alexis-Klod Klero. Euler tus thib ob tus tub, Carl, kawm tshuaj nyob rau hauv Halle, thiab lub thib peb, Christoph, los ua ib tug tub ceev xwm. Nws tus ntxhais Charlotte yuav ib tug Dutch aristocrat thiab nws tus niam laus Helena nyob rau hauv 1777 - ib tug Lavxias teb sab tub ceev xwm.

King intrigues

Kev sib raug zoo paub txog Frederick II twb tsis yooj yim. Qhov no yog tej zwj ceeb nyob rau ib tug tseem ceeb sib txawv nyob rau hauv lub tus kheej thiab philosophical leanings Frederick - ib tug zoo siab, nws tus kheej-kaj siab lug, elegant thiab witty conversationalist, ib tug sympathizer ntawm Fabkis Enlightenment; mathematician Euler - ib tug coj, ntse, earthy thiab devout Protestant. Lwm, tej zaum tseem ceeb vim li cas yog lub resentment ntawm Leonard hais tias nws twb yeej tsis muaj tus ncej ntawm tus thawj tswj hwm ntawm lub Berlin Academy. Qhov no resentment tau xwb zus tom qab ncaim lub Maupertuis thiab Euler lub dag zog kom lub tsev afloat, thaum Frederick sim nyiam cov thawj tswj lub rooj zaum Jean d'Alembert Leron. Cov yav tas, nyob rau hauv qhov tseeb, tuaj rau Berlin, tab sis tsuas yog qhia rau cov King txog nws nim and Share Leonard. Friedrich yog tsis tsuas tsis quav ntsej li lub tswv yim ntawm D'Alembert, tab sis pointedly tshaj tawm hais tias nws tus kheej lub taub hau ntawm lub academy. Qhov no, nrog rau ntau ntau lwm yam failures ntawm tus huab tais, thaum kawg, coj mus rau lub fact tias cov biography ntawm mathematician Euler ua ib tug ntse tig rov qab.

Nyob rau hauv 1766, nyob rau hauv kev phem ntawm lub obstacles nyob rau ib feem ntawm cov huab tais, nws tshuav Berlin. Leonard tau txais caw qhov uas Catherine II rov qab mus rau St. Petersburg, qhov uas nws tau officially txais tos rov qab.

Ib zaug ntxiv, St. Petersburg (1766-1783)

Revered thiab adored nyob rau academy ntawm lub tsev hais plaub ntawm Catherine tus poj mathematician Euler ua hauj lwm tsis tshua muaj neeg prestigious ncej thiab yog influential nyob rau hauv uas nws twb tsis kam muab rau li ntev nyob rau hauv Berlin. Nyob rau hauv qhov tseeb, nws ua si lub luag hauj lwm ntawm sab ntsuj plig thawj coj, yog hais tias tsis yog lub taub hau ntawm lub academy. Tu siab, txawm li cas los, cov kev kho mob nws tsis txhua yam mus zoo li ntawd. cataract ntawm sab laug qhov muag, uas pib mus thab nws nyob rau hauv Berlin twb ua ntau loj heev, thiab nyob rau hauv 1771 Euler txiav txim siab rau kev phais. Nws tsim nyog tau yog tus tsim ntawm ib tug rwj, uas yuav luag tag pov tseg lub zeem muag.

Tom qab ntawd tib lub xyoo, thaum lub sij hawm zoo kawg hluav taws nyob rau hauv St. Petersburg, nws ntoo lub tsev tsoo, thiab yuav luag qhov muag tsis pom Euler yuav tsis tau hlawv ciaj sia tsuas ua tsaug rau lub heroic cawm ntawm Peter Grimm, ib tus kws txawj txua los ntawm Basel. Yuav kom alleviate txoj kev nyuaj siab, lub Empress tau faib cov nyiaj rau qhov kev siv ntawm ib lub tsev tshiab.

Lwm hnyav tshuab hlob Euler nyob rau hauv 1773 thaum nws tus poj niam tuag lawm. Tom qab 3 lub xyoo, tsis tau nyob ntawm seb lawv cov me nyuam, nws yuav ib tug thib ob lub sij hawm nyob rau hauv nws ib nrab tus muam, Xas Los Mes Anpikayi Gsell, (1723-1794).

Txawm tias tag nrho cov neeg tuag taus cov txheej xwm, cov mathematician Leonhard Euler twb mob siab rau science. Tseeb, hais txog ib nrab ntawm nws ua hauj lwm tau luam tawm los yog tau yug los nyob rau hauv St. Petersburg. Ntawm lawv yog cov ob ntawm nws "bestseller" - "Cov tsiaj ntawv mus rau ib tug German Princess" thiab "Algebra." Lawm, nws yuav tsis ua tsis muaj ib tug zoo secretary thiab cov kev pab uas nws tau muab, cov lwm yam, Nicklaus fuss, ib tug compatriot ntawm Basel thiab lub neej yav tom ntej tus txiv ntawm tus ntxhais xeeb ntxwv uas Euler. Active ib feem nyob rau hauv tus txheej txheem ntawm kev noj nws tus tub Johann Albrecht. Cov yav tas kuj ua raws li ib tug stenographer Academy zaug nyob rau hauv uas ib tus paub txog, raws li ib tug tag nrho cov tswv cuab ntawm cov hiob, yuav tsum tau tswj.

tuag

Qhov zoo mathematician Leonhard Euler tuag ntawm ib tug mob stroke 18 Cuaj hlis 1783 thaum uas ua si nrog nws cov tub xeeb ntxwv. Nyob rau hnub ntawm txoj kev tuag ntawm nws ob tug loj slates twb pom cov qauv uas qhia txog ib tug zais pa ya davhlau, lub zoo meej rau hli ntuj 5, 1783 nyob rau hauv Paris, lub Montgolfier cov kwv tij. Lub tswv yim twb tsim thiab npaj rau cov ntawv qhia los ntawm Johann tub. Nws yog tus kawg los ua ib tus paub txog, luam tawm nyob rau hauv 1784 Memoires volume. Leonhard Euler thiab nws tau pab rau kev kawm txog zauv yog li ntawd zoo kawg hais tias cov khiav ntawm cov khoom tos lawv tig nyob rau hauv kev kawm ntawv txhua hnub, tau luam tawm rau 50 xyoo tom qab kev tuag ntawm tus paub txog.

Kev ua si nyob rau hauv Basel

Tsis pub dhau ib tug luv luv lub sij hawm ntawm Basel Euler pab mus rau kev kawm txog zauv yog ib qho yooj yim rau isochronous thiab kev sib nrig sib curves, raws li zoo raws li kev ua hauj lwm nyob rau hauv kev sib tw nqi zog ntawm lub Paris Academy. Tab sis lub ntsiab teeb meem nyob rau ntawm no theem yog tus Dissertatio Physica de sono, yuav tsum yog nyob rau hauv them nyiaj yug ntawm nws nomination rau lub rooj zaum ntawm physics ntawm lub University of Basel, nyob rau hauv qhov thiab muab faib rau ntawm lub suab, nyob rau hauv particular, tus ceev ntawm lub suab thiab lub cim ntawm cov suab paj nruas seev.

Tus thawj St. Petersburg lub sij hawm

Dua li ntawm qhov noj qab haus huv tej teeb meem txog tej ntawm Euler, nce qib nyob rau hauv kev kawm txog zauv, tus paub txog yuav tsis tab sis ua surprise. Thaum lub sij hawm lub sij hawm no, nyob rau hauv tas li ntawd mus rau lub yooj yim hauj lwm nyob rau mechanics, lub hom phiaj ntawm cov suab paj nruag, raws li zoo raws li naval architecture, nws tau sau 70 cov khoom ntawm ntau yam kev xai ntawm zauv tsom xam thiab kev tshawb xav tooj kom meej teeb meem nyob rau hauv physics, mechanics thiab astronomy.

Ob tug tagnrho ntawm "Txhua yam" yog thaum pib ntawm ib tug nyob deb-xeeb lub hom phiaj ntawm kev rov xyuas dua ntawm tag nrho cov yam ntawm mechanics, nrog rau cov mechanics ntawm khoom, saj zawg zog thiab elastic lub cev, raws li zoo raws li cov dej thiab xilethi-aus mechanics.

Raws li yuav pom los ntawm qhov kev ceeb toom-phau ntawv Euler, tseem nyob rau hauv Basel, nws xav tias ib tug ntau yam txog suab paj nruag thiab suab paj nruas muaj pes tsawg leeg thiab twb npaj mus sau ib phau ntawv. Cov kev npaj tau matured nyob rau hauv St. Petersburg thiab muab sawv mus ua hauj lwm rau Tentamen, luam tawm nyob rau hauv 1739. Cov khoom pib nrog ib tug kev sib tham txog qhov ntawm lub suab raws li deeg ntawm huab cua hais, nrog rau nws cov tis, physiology thiab hnov xaav ntawm lub suab tiam los ntawm txoj hlua thiab cua seev.

Cov tub ntxhais ntawm lub chaw ua hauj lwm yog lub hom phiaj ntawm Library tshwm sim los ntawm cov suab paj nruag uas Euler tsim los ntawm qhov chaw kawm lub luv tones, chords los yog sequences ntawm suav qhov tseem ceeb, raws li ntawm constituting "kev zoo" ntawm cov suab paj nruas qauv: lub sab rau theem, ntau dua qhov lub Library. Lub chaw ua hauj lwm yog ua li cas nyob rau hauv lub ntsiab lus teb ntawm ib tug nyiam sau diatonic chromatic luv, tab sis kuj muab ib tug ua tiav zauv hom phiaj ntawm temperaments (ob ancient thiab niaj hnub). Euler tsis yog tus tsuas yog ib qho uas sim tig music rau hauv lub caij nyoog kev kawm: Descartes, Mersenne, thiab ua ib yam nkaus rau nws, raws li D'Alembert, thiab ntau lwm tus neeg tom qab nws.

Lub ob-volume Scientia Navalis - lub thib ob theem ntawm nws txoj kev loj hlob ntawm muaj kuab mechanics. Cov phau ntawv qhia txog tej ntsiab cai thiab kev hydrostatic equilibrium kev tshawb xav ntawm deeg thiab peb-dimensional lub cev uas yog immersed nyob rau hauv dej. Ua hauj lwm muaj pib mechanics ntawm cov khib nyiab, uas tom qab crystallizes nyob rau hauv phau ntawv Theoria Motus corporum solidorum seu rigidorum, peb loj treatise rau mechanics. Qhov thib ob ntim ntawm cov kev tshawb xav siv rau ships, shipbuilding thiab navigation.

Tiam Leonhard Euler, kev kawm nyob rau hauv kev kawm txog zauv uas nyob rau hauv no lub sij hawm tau impressive, muaj lub sij hawm thiab muaj lub zog mus sau ib tug 300-page ua hauj lwm rau elementary xam rau siv nyob rau hauv St. Petersburg lub tsev kawm ntawv. Yuav ua li cas muaj hmoo cov me nyuam uas yog qhia tau ib tug scholar kuj zoo kawg!

Berlin ua hauj lwm

Nyob rau hauv tas li ntawd mus rau lub 280 cov khoom, ntau ntawm cov uas twb tseem ceeb heev nyob rau hauv lub sij hawm no lub mathematician Leonard Euler tsim ib tug series ntawm landmark kev treatises.

Qhov teeb meem ntawm brachistochrone - nrhiav txoj hau kev uas taw tes loj tsiv los ntawm lub ntiajteb txawj nqus ntawm ib tug taw tes nyob rau hauv ib ntsug dav hlau mus rau lwm nyob rau hauv lub sij hawm shortest - ib tug thaum ntxov piv txwv ntawm ib qho teeb meem uas tsim los ntawm Johann Bernoulli nrhiav nuj nqi (los yog nkhaus), uas optimizes lub analytical qhia nyob ntawm seb cov kev ua. Nyob rau hauv 1744-m, ces nyob rau hauv 1766-m Euler ntau qhaub li qhov teeb meem no los ntawm kev tsim ib tug tseem tshiab ceg ntawm kev kawm txog zauv - "calculus ntawm variations".

Ob tug me treatise rau lub trajectories ntawm planets thiab comets thiab optics, tau tshwm sim txog 1744 thiab 1746 xyoo. Cov yav tas yog ntawm cov keeb kwm kev txaus siab, vim nws tau pib ib tug kev sib tham nyob rau hauv lub Newtonian hais thiab nthwv dej kev tshawb xav ntawm lub teeb Euler.

Nyob rau hauv deference rau nws chaw ua hauj lwm, King Frederick II, Leonard muab qhov tseem ceeb ua hauj lwm rau ballistics Englishman Benjamin Robins, txawm hais tias nws tsis ncaj ncees criticized nws "Txhua yam" nyob rau hauv 1736 Nws ntxiv, txawm li cas los, thiaj li muaj ntau cov lus, explanatory sau ntawv thiab kho, raws li ib tug tshwm sim ntawm phau ntawv "Artillery" (1745) by volume yog 5 lub sij hawm ntau dua li cov tseem cia nrog.

Lub ob-volume "Introduction to infinitesimal tsom xam" (1748), mathematician Euler tso tsom xam raws li ywj siab kev qhuab qhia, tshab xyuas nws ntau discoveries nyob rau hauv lub teb ntawm infinite series, infinite khoom thiab txuas ntxiv cov zauv feem. Nws muaj ib tug ntshiab pom kev muaj nuj nqi tiag tiag thiab complex qhov tseem ceeb thiab kev siv lub luag hauj lwm nyob rau hauv lub tsom xam ntawm tus xov tooj e, exponential thiab logarithmic zog. Qhov thib ob ntim yog nplooj siab mus rau lub analytical geometry: kev tshawb xav ntawm algebraic curves thiab tej chaw.

"Txawv calculus" kuj muaj ob qhov chaw, tus thawj uas yog mob siab rau mus rau lub xam ntawm sib txawv thiab differentials, thiab lub thib ob - lub hom phiaj ntawm lub hwj chim series summation mis thiab nrog ib tug loj tus naj npawb ntawm cov piv txwv. Ntawm no, incidentally, muaj cov thawj luam Fourier series.

Lub peb-volume "Integral calculus" mathematician Euler xav quadrature (m. E. Txom iteration) elementary zog thiab technology coj lawv linear differential sib npaug, ib tug paub piav qhia txog ntawm lub hom phiaj ntawm linear differential sib npaug ntawm ob txhais kev txiav txim.

Thoob plaws hauv lub xyoo nyob rau hauv Berlin, thiab tom qab ntawd Leonard kawm geometrical optics. Nws cov khoom thiab cov phau ntawv rau cov kawm, nrog rau cov monumental peb-volume "Dioptrics" li cas mus rau xya tagnrho ntawm Opera Omnia. Lub hauv paus ntsiab lus ntawm no ua hauj lwm yog los txhim kho lub kho qhov muag seev xws li telescopes thiab rub kom pom loj, yuav ua li cas los daws kom tau lub chromatic thiab kheej kheej aberration los ntawm ib tug complex system ntawm lo ntsiab muag thiab sau kua.

Euler (mathematician): Nthuav lus tseeb ntawm lub thib ob St. Petersburg lub sij hawm

Nws yog tus tshaj plaws tsim lub sij hawm, thaum lub sij hawm uas tus paub txog tau luam tawm ntau tshaj 400 cov ntaub ntawv nyob rau hauv cov ntsiab lus twb hais, raws li tau zoo raws li geometry, muaj tseeb kev tshawb xav thiab txheeb cais, kuas, thiab txawm nyiaj laus cov nyiaj rau cov poj ntsuam thiab ua liaj ua teb. Ntawm lawv muaj peev xwm yuav muab faib ua peb treatises rau algebra, cov kev tshawb xav ntawm lub hli thiab naval science, raws li zoo raws li nyob rau lub hom phiaj ntawm tus xov tooj, tej yam ntuj tso philosophy thiab dioptrics.

Ntawm no tuaj lwm ntawm nws "bestseller" - "Algebra." Lub npe mathematician Euler kho no 500-page ua hauj lwm, uas yog sau ntawv nrog lub hom phiaj ntawm cov kev qhuab qhia yog qhia kom cov ib tug meej beginner. Nws rov rau hauv phau ntawv rau cov hluas apprentice, uas tau coj nrog nws los ntawm Berlin, thiab thaum twg lub chaw ua hauj lwm tiav lawm, nws to taub tag nrho tshaj thiab muaj peev xwm heev yooj yim daws tau algebraic teeb meem nyiag rau nws.

"Qhov thib ob kev tshawb xav ntawm ships" twb tseem tsim rau cov neeg uas tsis muaj kev paub ntawm kev kawm txog zauv, namely - cov neeg tsav nkoj. Nws yog tsis xav tsis thoob hais tias tus ua hauj lwm tau zoo heev ua tsaug rau lub extraordinary didactic txawj ntawm tus sau. Minister ntawm cov rog thiab Fabkis nyiaj txiag Anne-Robert Turgot npaj rau tus Vaj Ntxwv Louis XVI yuav tsum tau tag nrho cov me nyuam kawm ntawv ntawm marine thiab artillery tsev kawm ntawv mus kawm Euler tus treatise. Nws yog heev tej zaum yuav hais tias ib tug ntawm cov menyuam kawm ntawv muab tawm rau Napoleon Bonaparte. Tus huab tais txawm them 1,000 rubles lej rau lub meej mom ntawm republishing lub chaw ua hauj lwm, thiab cov Empress Catherine II, tsis xav kom muab nyob rau hauv rau tus vaj ntxwv, tau ob npaug tus nqi, thiab cov poj mathematician Leonhard Euler ntxiv tau txais 2000 rubles!