Intaai wowonod montok do Sidsimban

'''Sidsimban''', mantad hogot sori<u>sid</u> 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' [[Ponompuuvan|'''sidsimban sompuuvan''']] (''integral calculus'') om [[Pongungaban|'''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'') <math>f</math>, ii poingkomoi id sopo poinlantop <math>[a, b]</math>. Haro nogi daa pampos <math>F</math> poingkomoi id ngai <math>x</math> suang <math>[a, b]</math> poingkaa:

<math>F(x) = \int_{a}^{x} f(t) \mathop{dt}</math>

om pointongkop donlombus (''uniformly continuous'') no <math>F</math> ontok <math>[a, b]</math>, om otungab (''differentiable'') ontok sopo poingukab <math>(a, b)</math> om otopot id saau:

<math>\frac{\mathop{d}}{\mathop{dx}} (F(x)) = f(x) \quad \forall x \in (a, b)</math>

om <math>F</math> nopo roitan do saaptungab (''antiderivative'') di <math>f</math>.

=== Hiob koduo ===

Hiob diti somoonu roitan do '''tibabar Newton-Leibniz'''.

Haro daa pampos kigatang totunud <math>f</math> ontok sopo poinlantop <math>[a, b]</math> om iso pampos donlombus <math>F</math> ontok <math>[a, b]</math> om pampos diti it saaptungab di <math>f</math> id <math>(a, b)</math> moi do:

<math>\frac{\mathop{d}}{\mathop{dx}} (F(x)) = f(x).</math>

Nung osompuuvan Riemann (''Riemann integrable'') ot <math>f</math> id <math>[a, b]</math> om kaanu no piiradan hingkaa:

<math>\int_{a}^{b} f(x) \mathop{dx} = F(b) - F(a).</math>

== Poomitanan: Koguraan don Newton ==

Koiyonon do iso tinan: <math>x(t)</math>. Mantad komoyon do siniau (''velocity''), siniau, <math>v(t)</math> nopo nga' i tungab koiso do koiyonon:

<math>v(t) := \frac{d}{dt} (x(t)) </math>

Om sinikap, <math>a(t)</math> (''acceleration'') nopo nga' i tungab koiso do siniau, om nogi i tungab koduo do koiyonon:

<math>a(t) := \frac{d}{dt} ( v(t)) = \frac{d^2}{dt^2} (x(t)) </math>

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

<math>j(t) := \frac{d}{dt} (a(t)) = \frac{d^2}{dt^2} (v(t)) = \frac{d^3}{dt^3} (x(t))</math>

== 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.