Sonli usullar

🟢 — masalani tezlashtiradi · 🟡 — ilg'or daraja · 🔵 — chuqur o'rganish (olimpiada darajasi)

🔵 Nyuton–Rafson usuli

$f(x) = 0$ ning ildiziga yaqinlashish:

$x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$

🟡 Trapetsiya qoidasi

$\int_a^b y\,dx \approx \frac{h}{2}\big[y_0 + 2(y_1 + y_2 + \dots + y_{n-1}) + y_n\big], \qquad h = \frac{b - a}{n}$

Egri chiziq botiq (∪) bo'lsa — ortiqcha, qavariq (∩) bo'lsa — kam baho beradi.

🔵 Simpson qoidasi ($n$ juft)

$\int_a^b y\,dx \approx \frac{h}{3}\big[y_0 + 4(y_1 + y_3 + \dots) + 2(y_2 + y_4 + \dots) + y_n\big]$