Sidsimban

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 

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 

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 

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 

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 
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.