I will be teaching a Multivariable Calculus undergraduate course soon. Usually, this course is taught through bibliography such as Marsden's and Tromba's "Vector Calculus" or Wood's "Advanced Calculus", which are great, but I would love for my class to be a bit more broad and challenging. Specifically, I would love for the class to be oriented, just enough, since it is mainly for physics undergrads, to (differential) geometry and topology. In particular, I think about Nakahara's "Geometry, Topology, and Physics" when I think about how to introduce the notion of a vector, an inner and outer product, reference frames, and all of those things. I believe you shouldn't wait until grad school and to decide you want to do gravity or mathematical physics in order to understand what a tensor is, and I'd like my course to be an introduction to those concepts.
Hence, before I start writing my own notes, I was wondering if someone knows any bibliography which boards multivariable calculus' topics in such a manner without being too advanced, such as Nakahara's. I've already looked at some and asked for my colleagues' recommendations and nothing close to what I'm looking for has popped out.