according to Wikipedia, there is a simple way to prove Brouwer's fixed point theorem from Stokes' theorem: see here. So I would like to present the former famous theorem (Brouwer's one) to my Calculus students using the latter famous one (Stokes'theorem)!
However, the link uses the formalism of manifolds and differential forms, material that my students don't know. Is there a way to rewrite the proof using only basic Calculus material (basically, everything in Stewart's Calculus is fine).
Sorry for the vagueness of the question. What students know: Line integrals of functions/ vector fields in space, Green's theorem (tangential and normal forms), surface integrals of functions/vector fields, Stokes' theorem in space (the curl version). A proof using the Divergence Theorem instead of Stokes'theorem would be acceptable and very welcomed!
