Instrumental Tricks
lrb.co.uk
lrb.co.uk
My understanding is that the act of internalizing the meaning of the exponents is a tremendous enabler of understanding; engineers of old achieved a better feel for the task than us moderns with all of the fancy software.
Restated: there may be some good pedagogy in having the initial course or two do things in a classical way ahead of moving on to all of the new methods.
Really nice comparison.