It's funny: I had the EXACT SAME PROBLEM !!!! Like "how is it science when a prof says: "this equation is too complicated too solve so let's erase these third and forth derivatives and pretend that it's the same - even if it's not - because that's all that we can do"

So I left the "physics" courses and went the "math" courses... only to learn 3 years later how to prove that this kind of approximation is mathematically sound indeed :-D