How common is it for Calc III curricula to start with partial derivatives?

Question

Our calc III professor is starting our 2nd lecture tomorrow with computing partial derivatives. Nothing regarding the implementation of partial derivatives in R3 is being discussed or taught yet. All we're literally learning is how to compute them. Based on what I've self-studied from Stewart's and Paul's OMN, this is usually taught a bit later after one knows, at the very least, how to graph in 3D.

Any red flags about this professor or is this a respectable decision, to focus on the computational skills necessary for the course prior to actually teaching us any concepts?

Answer 1

That's how my class did it last semester.

I liked doing it before graphs because it let us basically use calc 1 curve sketching techniques in 3D.

Partial derivatives give you some directional slopes

Answer 2

It’s not how I do it, but it’s not outrageous either. He probably intends to weave in the ideas about how to deal with 3d functions as they become relevant in a discussion of calculus.

For comparison, I do something similar with the series unit of calc 2. I go straight into Taylor series and then introduce the relevant convergence tests and related ideas as they come up

Answer 3

It's not a crazy idea.  You can think of it as calc I derivatives are a narrative that starts with limits, works through secant / tangent lines and the difference quotient to arrive at the definition of a derivative, then (typically) gives you a whole set of derivative calculation rules without trying to rigorously prove why e.g. the quotient rule works the way it does.

So here, it's like you are watching a sequel, and this professor knows that the rules for calculation will be most frequently used going forward, so they want to get to that point quickly.

Answer 4

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