My Calc 3 (and Calc 2) professor often likes to implement his own notation for things that have “standard” notations. He deviates from our text A LOT, but this time, I wonder if he’s gone too far. We started learning about partial derivatives yesterday, and instead of the traditional “round d” notation, he’s using D_1(f), D_2(f), etc. He gave us the following notes to go over as to why he feels standard notation is wrong. Now my classmates and I don’t have enough background to even know what he’s talking about (since we’re just now learning the topic to begin with) but some of us suspect he might be wrong. Is there anyone that can look through this briefly and explain whether he is right or wrong, and why?
Edit: I guess my question comes down to “is his argument against partial d notation valid” not whether the D_i notation is valid, which seems to be the case that it is.