If you teach multivariable calculus, do you incorporate differential forms as an option to traditional vector calculus? Just curious. #ITeachMath #Calculus #VectorCalculus #DifferentialForms

#Mechanical #Circuits

As an EE, I take pride in the fact that, although ME came before us and CE before them, much of the #engineering formalism arose in the 19th Century in the electrical context. Much of engineering theories are shared between #EE, #ME, and #CE, and at the core is #VectorCalculus and #AbstractAlgebra. This video shows one such connection.

https://youtu.be/Zv9Q7ih48Uc

GENERALIZED STOKES THEOREM:
The integral of a differential form $\omega$ over the boundary $\partial \mathrm{\Omega }$ of some orientable manifold $\mathrm{\Omega }$ is equal to the integral of its exterior derivative $d\omega$ over the whole of $\mathrm{\Omega }$.
$${\displaystyle {\int }_{\partial \mathrm{\Omega }}\omega ={\int }_{\mathrm{\Omega }}d\omega }$$
#VectorCalculus #DifferentialGeometry #MultivariateCalculus #Calculus #StokesTheorem #GeneralizedStokesTheorem #Calculus #FundamentalTheorem #Manifold #Boundary #ExteriorDerivative #Stokes