Vector Calculus Formulas

Line Integrals

Flux Along a Curve

Work/Flow/Circulation

Path Integrals for Conservative Fields

Conditions for Conservative Fields

Green's Theorem (Circulation-Curl or Tangential Form)

Green's Theorem (Flux-Divergence or Normal Form)

Green's Theorem Area Formula

Surface Area Definition

Surface Area of a Parametrized Surface defined as r(u,v)

Surface Area of an Implicit Surface or Level Surface defined by f(x,y,z) = c

Surface Area of an Explicit Surface defined by z = f(x,y)

Surface Integral of a Scalar Function where S is defined parametrically by r(u,v)

Surface Integral of a Scalar Function where S is defined implicitly by f(x,y,z) = c

Surface Integral of a Scalar Function where S is defined explicitly by z = f(x,y)

Stokes' Theorem

curl F

div F

Stokes' Theorem: ndsigma for implicit surfaces defined by f(x,y,z) = c

Stokes' Theorem: ndsigma for parametrized surfaces defined by r(u,v)

Divergence Theorem