Is anyone here fluent at explaining Calculus?

[Chaotic42]

Buy it, read it, love it.

Did you take a look at this? I'm serious, it's an extremely useful book if you're going to be in Calculus for a while or if you really want to try and understand it.

 

[Gibson486]

Calc 1 is hard for lots because you actually have to know how to do it. In high school, you can just memorize the steps to solve Algebra problems. Infact, that is how some kids are taught it today. here are the steps to solve..."1...2...3". This may even go to Pre Calc, where they just in grain your head how to solve for a limit. You know how to solve for it, but you have no idea what the hell it is for and when you encounter something out of the ordinary, GAME OVER!

In college, you no longer get "steps" to solve. They tell you plain and simple...."This is an integral, these are the rules....now solve it". If you came from a "steps" background, it is going to be challenge to get out of that rut. This is the biggest problem I saw when i used to tutor people. They would fail because they did not know how to apply rules to problem without me telling them how to.

And yes, College level 101 math classes are boring, but that is why it can be hard to teach it. The dude (or dudets) teaching it are math people who usually know their stuff. To them, calc 1 is a joke. They cannot understand how you can not find the derivatives. It is so elementry to them that they are as bored teaching it as you are learning it. That is what happens when you become a "master" at your "domain". You suddenly loses your sense of how difficult you had it when you started out.

 

[Gibson486]

Did you take a look at this? I'm serious, it's an extremely useful book if you're going to be in Calculus for a while or if you really want to try and understand it.

That book series is awesome! In college, I partied while I took calc 3. This meant sleep during class and studying beers during HW. I just read the sections I needed the day before tests and final and I passed.

 

[Q]

I am pretty terrible at math, and somehow ended up taking 5 math courses and got B's in all of them. Not sure how that relates to the thread, other than the fact that you can do more than you think you can.

 

[iCyborg]

My prof from Calc 1 said that to fully grasp limits and continuity requires some mathematical maturity. And I agree, most people who think Calc 1 is easy usually learn some rules and how and when to apply them, but it's a whole another thing to understand why exactly are limits/continuity/derivatives defined just the way they are in epsilon-delta form, and not in some other way.

I understand those two, as the function does not need to be continuous on an interval for there to be a limit on said interval.

You probably mean it doesn't need to be continuous in a point for there to be a limit in that point. As is, the sentence doesn't make much sense

Luckily continuity (what we're doing now) is a lot easier than defining these stupid things,

Hm, a function is continuous in a point if there's a limit in that point and is equal to the value of the function in that point. Formally, limits are crucial for the notion of continuity, I can't see how would it be (a lot) easier conceptually...

Yeah, you seem to get how it works in your images, it's all good...

 

[BlackTigers]

Erm, that's what I meant....hahaha. I can visualize everything....just need to work on explaining why things happen when I move numbers around. It's getting a little better now...it's no longer foreign, I just have to get all the terms right.

Tomorrow I have some more proofs that I hope you guys can look over for me....namely the IntermediateValueTheorem and proving roots. And I lied, continuity isn't easier, it's just different. I have to prove everything in the exact same way, but it's getting a little better.

Either way, after working with my professor for 15 minutes everything started to gel. What took me 6 hours to do last night, I breezed through in 20 minutes today.