I started with optimization this year. Namely, Dan’s taco cart problem.
Why? Because if you have to cut off learning when the semester ends, then you’ve got to present the most important stuff first. Why? So they have time to actually processes it.
No one cares until it’s a story, and the text-book order is as about as good a narrative as a Goosebumps book.
For instance, when attempting to solve the taco cart problem, you end up with a term that looks like:
This is the perfect time to introduce the chain rule. Why? Because it’s also one of the most important concepts in calculus, and the instructor’s obsessions with linearity of curriculum is no the students’.
Also, at BIG, a student is building a robotic model of Thing from Adam’s family that’s controlled remotely by myoelectric sensors.