"सदिश कलन" (अनुभाग) सम्पादित करें

== प्रमुख प्रमेय ==

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! Theorem !! Statement !! Description
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! ग्रेडिएन्ट प्रमेय (Gradient theorem)
| <math> \varphi\left(\mathbf{q}\right)-\varphi\left(\mathbf{p}\right) = \int_L \nabla\varphi\cdot d\mathbf{r}. </math> || The [[line integral]] through a gradient (vector) field equals the difference in its scalar field at the endpoints of the [[curve]].
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! ग्रीन का प्रमेय (Green's theorem)
| <math>\int_{C} L\, dx + M\, dy = \iint_{D} \left(\frac{\partial M}{\partial x} - \frac{\partial L}{\partial y}\right)\, dA</math> || The integral of the scalar curl of a vector field over some region in the plane equals the line integral of the vector field over the curve bounding the region.
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! स्टोक का प्रमेय (Stokes' theorem)
| <math> \int_{\Sigma} \nabla \times \mathbf{F} \cdot d\mathbf{\Sigma} = \oint_{\partial\Sigma} \mathbf{F} \cdot d \mathbf{r}, </math> || The integral of the curl of a vector field over a [[surface]] equals the line integral of the vector field over the curve bounding the surface.
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! डाइवर्जेंस प्रमेय (Divergence theorem)
| <math>\iiint\limits_V\left(\nabla\cdot\mathbf{F}\right)dV=\iint\limits_{\partial V}\mathbf{F}\cdot d\mathbf{S},</math> || The integral of the divergence of a vector field over some solid equals the integral of the [[flux]] through the surface bounding the solid.
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