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Sidsimban

Mantad Wikipedia

Sidsimban, mantad hogot sorisid om simban (Boros Inggilis: calculus) nopo nga' iso raan gana' pongintaban ii poingimurio' id sorisid do gatang minsimban, lobi po kokomoi kopoilaan kosimbanan dau ugu sinikap simban. It duo raan tagayo do sidsimban nopo nga' sidsimban sompuuvan (integral calculus) om sidsimban tungab (differential calculus). It tibabar (theorem) toponsol id sidsimban nopo nga' roitan do tibabar timpou sidsimban (fundamental theorem of calculus).

Tibabar timpou

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It tibabar timpou sidsimban momisunud do piomutan di ponompuuvan miampai pongungaban. Haro duo hiob (toi boogian) do tibabar diti. It hiob koiso, roitan do tibabar timpou sidsimban koiso nopo hingkaa:

Hiob koiso

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Haro daa pampos donlombus kigatang totunud (continuous real-valued function) , ii poingkomoi id sopo poinlantop . Haro nogi daa pampos poingkomoi id ngai suang poingkaa:

om pointongkop donlombus (uniformly continuous) no ontok , om otungab (differentiable) ontok sopo poingukab om otopot id saau:

om nopo roitan do saaptungab (antiderivative) di .

Hiob koduo

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Hiob diti somoonu roitan do tibabar Newton-Leibniz.

Haro daa pampos kigatang totunud ontok sopo poinlantop om iso pampos donlombus ontok om pampos diti it saaptungab di id moi do:

Nung osompuuvan Riemann (Riemann integrable) ot id om kaanu no piiradan hingkaa:

Poomitanan: Koguraan don Newton

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Koiyonon do iso tinan: . Mantad komoyon do siniau (velocity), siniau, nopo nga' i tungab koiso do koiyonon:

Om sinikap, (acceleration) nopo nga' i tungab koiso do siniau, om nogi i tungab koduo do koiyonon:

Haro nogi iso ginumu, roitan do sinikog (jerk) i nogi tungab koiso do sinikap, tungab koduo do siniau, om tungab kotolu do koiyonon:

Sidsimban don kumawo

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Sidsimban don kumawo (variational calculus) nopo nga' iso woyoguno do sidsimban id tantaban moyo kumawo (variations). Om iti ngai kumawo nopo nga' i sinimban do pampos om pamampos (functionals) do mokitimpak om mokilasut (maxima and minima) do pamampos. I sidsimban koubasan lobi poingotul id sinimban do gatang do pampos, nga' i sidsimban don kumawo poporuhang do totulan id sinimban do pampos sondii, okon nopo sinimban do gatang dau.

Id sidkamot, poomitanan do sidsimban don kumawo nopo nga' koguraan don Lagrange.