> for someone studying vector calculus properly If you can’t invert vectors, you aren’t studying vector calculus properly. ;-) Differential forms are a half-b

> for someone studying vector calculus properly If you can’t invert vectors, you aren’t studying vector calculus properly. ;-) Differential forms are a half-baked formalism. Unfortunately I don’t know of any great undergraduate level geometric calculus textbooks. Ideally there would be something like Hubbard & Hubbard’s book (http://matrixeditions.com/5thUnifiedApproach.html http://matrixeditions.com/5thUnifiedApproach.html) written using GA as a formalism. Hestenes & Sobczyk’s book (http://geocalc.clas.asu.edu/html/CA_to_GC.html http://geocalc.clas.asu.edu/html/CA_to_GC.html) is a hard slog, and not appropriate for an undergraduate audience.