Formulari de càlcul

$\int u\,dv = uv - \int v\,du$

la que se simplifica en derivar-se

$\int f(g(x))g'(x)\,dx = \int f(u)\,du$

$\int \dfrac{dx}{ax+b} = \dfrac{1}{a}\ln|ax+b| + C$

descompon el denominador en factors

l'altra variable es tracta com una constant

$\nabla f = \left(\dfrac{\partial f}{\partial x}, \dfrac{\partial f}{\partial y}\right)$

$\nabla f = \vec{0}$

$H = f_{xx}f_{yy} - (f_{xy})^2$

$H > 0 \text{ i } f_{xx} > 0$

$H > 0 \text{ i } f_{xx} < 0$

$H < 0$

$\iint_R f\,dA = \int_a^b\!\!\int_c^d f(x,y)\,dy\,dx$

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

hi ha arrel si $f(a)\cdot f(b) < 0$

$\int_a^b f \approx \dfrac{h}{2}\left[f_0 + 2f_1 + \cdots + 2f_{n-1} + f_n\right]$

$\dfrac{h}{3}\left[f_0 + 4f_1 + 2f_2 + \cdots + f_n\right]$