Nambala ya Euler (e)

Number e (kapena, monga imatchedwanso, nambala ya Euler) ndiye maziko a logarithm yachilengedwe; masamu osasinthasintha omwe ndi nambala yopanda nzeru.

e = 2.718281828459…

Njira zodziwira nambala e (chilinganizo):

1. Kupyolera mu malire:

Malire achiwiri odabwitsa:

Njira ina (yotsatira njira ya De Moivre-Stirling):

2. Monga ndalama zotsatizana:

nambala katundu e

1. Malire ogwirizana e

2. Zowonjezera

Chochokera ku exponential function ndi exponential function:

(e ^x) = ndi^x

Chochokera ku ntchito yachilengedwe ya logarithmic ndi ntchito yosinthira:

(log_e x)' = (ln x)" = 1/x

3. Zowonjezera

Kuphatikizika kosatha kwa ntchito ya exponential e ^x ndi exponential ntchito e ^x.

∫ ndi^x dx = ndi^x+c

Kuphatikizika kosatha kwa logarithmic function log_e x:

∫ chipika_e x ndi dx = ∫ ndix ndi dx = x ln x-x +c

Zotsimikizika zenizeni za 1 ku e ntchito yosiyana 1/x ikufanana ndi 1:

Logarithms yokhala ndi maziko e

Natural logarithm ya nambala x amatanthauzidwa ngati maziko a logarithm x ndi maziko e:

ln x = chipika_e x

Exponential Function

Ichi ndi ntchito yofotokozera, yomwe imatanthauzidwa motere:

f (x) = exp (x) = e^x

Euler formula

Nambala yovuta e ^{ndi a} zofanana:

e^{ndi a} = kodi (θ+ i tchimo (θ)

kumene i ndi gawo lolingalira (muzu wapakati wa -1), ndi θ ndi nambala yeniyeni.