I believe that math courses that incorporate modern computing can train future scientists to be better users of mathematics. Modern computing helps make the subject more concrete and can help with fast accurate and more difficult calculations. I hope Advanced Calculus using Mathematica takes a step in that direction.
We developed the basic material in Advanced Calculus using Mathematica over 20 years of teaching a second semester calculus course for engineering students. This made vectors and partial derivatives available before they were taught in physics and engineering courses. This worked especially well for students who took this course and physics in their second semester. The course ended with the 2D treatment of divergence and "swirl" in order to leave time for material on infinite series. There is a sample syllabus for the course in the eText.
Students with their lexicons at a final lecture
Those engineering students took a brief matrix algebra course and differential equations before returning to vector calculus. (Chemical and biomedical engineering students did not take the 5th course, but did study mathematical conservation of energy in 2D in the second semester course.) The additional background before the 5th course allowed for a deeper treatment of MAX-min in several variables and additional time on divergence and curl topics. There is a sample syllabus for that course in the eText.
Since the eText is free to students with a site license and comprised of stand-alone Notebooks, an instructor could use portions of the text as small as one of the interactive Notebooks that illustrate the various cases of tangency or to animate the flow of a vector field or show the osculating circle or show surface curvature or microscopic divergence or curl in 2D or 3D. They could also use a single chapter like basic vectors to enhance visualization and the algebra <-> geometry connection.
The eText contains many topics that are often not found in elementary texts and could be used as a reference for those topics:
Constrained first and second partial derivatives.
Linearization of the pendulum.
Local flows and inverse functions.
Functional dependence.
Vector potentials.
Higher dimensional MAX-min including bordered Hessians.