Doing Calculus 2 this semester, should I care about mathematical

>>7804219
Studying Mechanical Engineering btw.

>>7804219
Not if you want to be an engineer.

>>7804219
Nah you wouldn't be able to grasp them anyway

>>7804219
Unless they will be asked in a test, I suggest only trying to understand them. This will help you understand how the formulas are "created" (i can't find a better term, my English sucks), will help you memorize the formulas themselves and also will serve as a way to check you wrote the right formula without missing any coefficient/variable/whatever. Although don't loose too much time on this, engineering is all about applying the right formula at the right time.

EE here, definitely check them, it'll make their application easier.

>>7804219
Since you're asking, you probably haven't experienced proof based mathematics before. It makes no sense to start in Calculus 2 because you'll have no foundation of other theorems. You're an engineer, so you wouldn't know this, but after Calculus 3, math undergrads are basically told to fuck themselves and relearn everything formally. In my analysis class we started with a handful of set theory axioms, and worked all the way up through Calculus 3 using only formal proofs and a bit more.
To even begin to understand a real proof on a Calculus 2 topic, you'll need to work from the axioms. Otherwise you're just doing halfassed proofs based on shitty theorems you haven't proven.

not really.

Proofs are a dreary necessary we need in order to make sure that we can use something to solve problems.

Oliver Heaviside was using Heaviside step functions to solve differential equations before anyone had formally "Proved" that they always worked, and Richard Feynman was using path integrals to solve problems before anyone "proved" that they were mathematically valid.

Sure it's necessary that someone proves these things just incase they aren't correct, but it's more important for a mathematician to be able to solve problems by applying and manipulating theorems and results in clever ways than to remember the proof for the weierstrauss theorem or compact mapping theorem.