CALC II

Variable change from x,y to u,v for this integral.

Variable change from x,y to r,θ for this integral.

Variable change from x,y,z to r,θ,z for this integral.

Variable change from x,y,z to r,θ,ϕ for this integral.

Divergance of a Vector field

Curl of a Vector field

Dorito² in front of a vector field not dot nor cross product

Conservatie Vector Field

Dorito infront of Phi. With Phi = C being an equipotential surface.

Integration of a scalar over a line integral

Integration of a vec field over a line integral

Conditions for this to be true?

F is smooth and D is simply connected.

Fund THRM for Line integrals

Positvely oriented region

Go on the boundary and the region is on your left

Green’s Theorem

Unit vector of the normal to a parametrized surface

Unit vector of the normal to a level surface

Surface integral for a function

Surface integral for a vector Field / FLux integral

Orientation of a boundary for stokes theorem

Up - Surface orientation

Forward - Orientation boundary

Left - Towards Surface

Stokes theorem

Gauss’s Theorem

Outward flux is positive in the left hand

Crit Point test

Directional Derrivative

Scalar