Yep. I'm real glad Hestenes has been championing VA/VC so hard. That first text is a perfect supplementary reading that any undergraduate should read. Who was the author?
I skipped the a few and went straight to the last PDF (the Survey) and coming from a stronger foundational math background, I felt right at home. (I'd imagine those who went down the physics route would be thrown off by the notation though, so I understand the author's preface). He mentions physics and CS applications, but I really think this has structural engineering applications as well -- e.g. R^4 seems like a perfect domain to explore bidirectional tensile and shear strength of materials (especially composite materials/aggregates), then perform some FEA with all of the simple operations within that come inherent to operating within the bounds of the 4-vector form. I mean that's a real trivial example (and I obviously don't know enough about structural engineering to make a good analogy) but it seems like one of those cases where you move the problem set lifted into another domain, perform your manipulation then finally lower back into your original (co-)domain. (Frequently done in algebraic topology, most famously by Perelman on Poincare)
I think there is a very good reason why structural engineers never see this type of thing, and it's because most structural engineers don't like math. They like clicking buttons in their CAD/FEA/BIM/<insert-latest-TLA> computer system.
The people who write those systems on the other hand enjoy this math very much, and tend to use Galerkin as a verb and will casually point out just how wonderful the Lax-Milgram theorem is.
Or open any of these and search for “Maxwell”: http://www.av8n.com/physics/maxwell-ga.htm http://arxiv.org/pdf/1101.3619.pdf http://ieeexplore.ieee.org/ielx7/5/6879517/06876131.pdf http://geocalc.clas.asu.edu/pdf/SpacetimePhysics.pdf http://faculty.luther.edu/~macdonal/GA&GC.pdf