This is one of the places where I disagree with the article. As an (experimental) physicist, I've always found the dx notation better to understand. When I aske

This is one of the places where I disagree with the article. As an (experimental) physicist, I've always found the dx notation better to understand. When I asked the professor about how it works, he called it a calculus (as in German Kalkül, set of rules to almost mechanically manipulate a mathematical expression, not to be confused with "Calculus"). Of course there exist proofs in terms of limits, or differential forms. But it is something one has to learn, just like div and curl and so on. We had very mathematically rigorous math lectures. I was able to do most of the proofs, but failed to calculate even a simple derivative when thinking in differential forms. (Maybe because I failed to see what is a function and what is a variable in the "mathematical" notation and misapplied the chain rule.) The other thing where I disagree is the part about avoiding word problems. I think the word problems were the only interesing part - how to translate a given physical situation into a differential equation and variables. Solving them is not really interesting - everything interesting for me has been solved before, so I can just ask around the hallway or punch it into a computer algebra system.