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

simbanai

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

simbanai

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

simbanai

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

simbanai

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

simbanai

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.