El nhamba e, Nhamba yaEuler kana kuti Napier inosanozivikanwa ndiyo imwe yenhamba dzinokosha uye dzinokosha dzisina musoro mundima dzemasvomhu nealgebra. Nhamba yakakosha muexponential function isingagone kumiririrwa nenhamba yakasikwa. Nhamba iyi ine maapplications makuru munyika yemasvomhu.
Nechikonzero ichi, isu tichakumikidza chinyorwa ichi kukuudza zvese zvaunoda kuziva nezve nhamba e, maitiro ayo uye kukosha kwayo.
nhamba e
Inhamba isina musoro uye hatigone kuziva kukosha kwayo chaiko nekuti ine nzvimbo dzisingaperi, saka inotorwa senhamba isina musoro. Mumasvomhu, tinogona kutsanangura nhamba e sehwaro hwechisikigo exponential function, dzimwe nguva inonzi neper base nekuti neper masvomhu ndivo vakatanga kuishandisa.
Nhamba iyi inodaidzwa kunzi nhamba isinganzwisisiki nekuti haigone kumiririrwa sereshiyo yezvikamu zviviri, nhamba yedesimali haiperi, uyewo inhamba yakapfuura nekuti haigone kumiririrwa semudzi we algebraic equation ine rational coefficients.
Mhando huru
Pakati pezvinhu zvikuru tinogona kutaura zvinotevera:
- Iyi inhamba yenondescript ine nhamba dzisingakwanisi kudzokororwa nguva nenguva.
- Nhamba dzenhamba e hadziteveri chero rudzi rwepateni.
- Inowanzonzi Napier's constant kana Euler's number.
- Inogona kushandiswa mumatavi akasiyana emasvomhu.
- Haikwanise kumiririrwa nenhamba mbiri.
- Iyo zvakare haigone kumiririrwa senhamba chaiyo yedesimali kana inodzokorodza desimalis.
Nyanzvi yemasvomhu ine mukurumbira uye yakakosha Leonhard Euler, mumwe wenyanzvi dzemasvomhu dzakasimba dzenguva dzese, akashandisa chiratidzo e mudzidziso yelogarithms muna 1727.. Sangana pakati pevara rekutanga rezita rako rekupedzisira uye zita renhamba yedu zvakangoitika. Rekodhi rekutanga kana kufungidzira kwenhamba e inowanikwa mumapepa esvomhu yakatanga ku1614, pakaburitswa Mirifici Logarithmorun Canonis yaJohn Napier. Zvisinei, kuenzanisa kwekutanga kwenhamba kwakawanikwa naJacob Bernoulli pakugadzirisa dambudziko rekufarira kwenguva refu muhuwandu hwekutanga hwakagadziriswa, izvo zvakaita kuti anzwisise uye adzidze muganhu we algebraic inokosha, uye kukosha kwayo kwakagadziriswa pa 2,7182818.
Leonard Euler ndiye akatanga kutanga kuziva nhamba nechiratidzo chemazuva ano, icho chinoenderana nebhii e, asi akakwanisa kuzvisuma makore gumi gare gare muMathematics Mechanics yake. Muchokwadi, iyo nhamba yakatanga kuwanikwa naLeonhard Euler, asi murume akazviwana muna 1614 aive muScotsman ainzi John Napier. Nekuda kwekuwanikwa kwake, kuwanda kunogona kutsiviwa nekuwedzera, kupatsanura nekubvisa uye kuwanza nechigadzirwa, kurerutsa manyorerwo ekuita masvomhu ekuverenga.
Zvivakwa nemashandisirwo enhamba e
Zvinhu zvinotevera zvinogona kushandiswawo setsananguro dze e.
- e ihuwandu hwekudzokororwa kwefactorials.
- e ndiwo muganho wekutevedzana kwematemu.
- Kuwedzera kwechikamu kwe e hakuna kujairana, asi mune zvakajairika zvikamu zvinoenderera, panogona kana kusave zvakajairika zvinoenderera mberi zvikamu.
- e haina musoro uye inodarika.
Mamwe maapplication anogona kushandiswa nhamba iyi ndeaya anotevera:
- Mune zvehupfumi, iyi ndiyo chaiyo nzvimbo yekutanga yekuverengera kufarira.
- Mubiology, kukwanisa kutsanangura kukura kwesero kwakakosha zvikuru.
- Kubudiswa kwe capacitor kunotsanangurwa mumagetsi.
- Inotsanangura kuvandudzwa kweiyo ionic concentrations kana maitiro mumunda we chemistry.
- Kutungamira kwenhamba dzakaoma, kunyanya fomula yaEuler.
- Carbon 14 kufambidzana kwemafossils mu paleontology.
- Kuyera kurasikirwa kwekupisa kubva kune zvinhu zvisingaite mumushonga we forensic kuona nguva yekufa.
- Munhamba, probability theory uye exponential function
- Muchiyero chegoridhe uye logarithmic spiral.
Nekuti inoonekwa mumabasa eexponential anotevedzera kukura, kuvepo kwayo kwakakosha patinodzidza kukurumidza kukura kana kudzikira, senge huwandu hwemabhakitiriya, kupararira kwechirwere, kana kuora kwemwaranzi, uye inobatsirawo pakupfimbana zvisaririra.
Kukosha uye kuziva
Nhamba e inenge yakaenzana ne2.71828 uye inowanzonyorwa se ≈2718. Huwandu uhu hwakakosha zvikuru mumasvomhu uye nezvimwe zvakawanda zvine chekuita nekugadzirwa, sainzi nehupenyu hwemazuva ese. Iyi nhamba inoita basa rakakosha kwazvo mumunda wecalculus. uye icho chikamu chezvakawanda zvakakosha mhedzisiro senge miganho, zvinobva, zvakabatanidzwa, zvakatevedzana, nezvimwe. Uyezve, ine seti yezvivakwa zvinobvumira kushandiswa kwayo kutsanangura mataurirwo ane zvakakosha mashandisirwo munzvimbo dzakawanda dzeruzivo rwevanhu.
Zvimwe zvekuda kuziva zvine chekuita nenhamba e ndezvinotevera:
- Nhamba e inoshanda sehwaro hwechisikigo kana kuti natural logarithmic system.
- Nhamba yacho inomiririrwa ne lnx = t, apo x inhamba chaiyo chaiyo, t inomiririra x> 1 uye yakaipa ye x <1.
- Iripo mutsanangudzo yebasa y(x) = ex kana y(x) = exp(x) ine CVA seti yemitengo inotenderwa ndiyo seti R yenhamba dzese chaidzo.
Dzimwe nhoroondo
Kutanga kusina kunanga kunhamba iyi kunowanikwa mubhuku raJohn Napier rine mukurumbira muna 1614, Mirifici Logarithmorum Canonis Descriptio, umo pfungwa dzake dzelogarithms, antilogarithms, mhedzisiro, nematafura avo ekuverenga anotanga kutsanangurwa; zvisinei, Jacob Bernoulli achawana yekutanga approximation nekugadzirisa dambudziko rekutanga rakagadziriswa chiyero chekufarira kwenguva refu, izvo zvinokuendesa kune iyo ikozvino inozivikanwa muganhu mushure mekudzokorora kunotevera.
Isa kukosha kwayo ku2,7182818. Nyanzvi yemasvomhu uye muzivi Gottfried Leibniz akazoshandisa kukosha uku mutsamba kuna Christian Huygens muna 1690 na1691, achiratidza nebhii b. Leonard Euler akatanga kuzivisa nhamba muna 1727 nechiratidzo chemazuva ano, vara e, asi hazvina kusvika makore gumi gare gare paakasuma nhamba yacho kunharaunda yemasvomhu mubhuku rake Mechanics.
Gare gare nyanzvi dzaizoshandisa a, b, c uye e kusvika iyo yekupedzisira yahwina yenhamba dzisina musoro. Charles Hermite akaratidza kuti iyi yaiva nhamba inokosha muna 1873. Kufungidzira kwavo kwakatanga nebasa raBernoulli, ipapo Euler akaita fungidziro yenzvimbo gumi nemasere mushure mecomma, saka vakagadzira, sekuona nzvimbo yepi, vhezheni yazvino yemakwikwi yaive muna 18 Shigeru Kondo naAlexander J. Yee vakatsunga. e kusvika kune bhiriyoni chaiyo nzvimbo dzedesimali.
Ndinovimba kuti neruzivo urwu unogona kudzidza zvakawanda nezve nhamba ye e uye maitiro ayo.