User:Lineintegral123

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Fundamentals of Calculus

Fund. Theorem of Calc: $\int_a^b f(x)\,dx\, = F(b) - F(a).$

Green's Theorem: $\oint_{C} (L\, \mathrm{d}x + M\, \mathrm{d}y) = \iint_{D} \left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right)\, \mathrm{d}x\, \mathrm{d}y.$

Stoke's Theorem: $\int_{\Sigma} \nabla \times \mathbf{F} \cdot d\mathbf{\Sigma} = \oint_{\partial\Sigma} \mathbf{F} \cdot d \mathbf{r},$

Divergence Theorem: $\iiint\limits_V\left(\nabla\cdot\mathbf{F}\right)dV=\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf{F}\cdot\mathbf{n}\,dS .$