Were you taught the formal definition of a limit of a function in Calc I?

[Random Variable]

Something like the following:

Let f : D->R and let c be an accumulation point of D. Then the limit of f at c is L iff for each e>0 there exists a d>0 such that |f(x)-L|<e whenever 0<|x-c|<d and x is an element of D.

or

The lim x->c f(x) = L iff for each neigborhood V of L there exists a deleted neighborhood U of c such that f(UnD) is a subset of V.

I don't remember what I was taught.

 

[Drakkon]

I took AP calc in high school and i didn't learn it there. But then when i took it again in college (didnt score high enough on the AP test) i did learn it there. I remember it specifically because 2 years later as i persued a degree in math i had to prove why that is true.
It was worded a LOT differently though in CAlc 1....like instead of accumulation point they used just "as x approaches" and the epsilon and sigma were just part of the limit equation.

 

[eakers]

yes
and we also weren't allowed to do integrals until we learned the proof for the fundamental theory of calculus :thumbsdown:

 

[silverpig]

Yep.

 

[esun]

Yes. I didn't understand it in high school, but we learned it.

 

[BrownTown]

actually we did limits in pre-calculus so I learned it there .

 

[spidey07]

I don't recall. All I recall is that I didn't totally understand Calculus until I had finished it and saw it's application to the world.

I still think people don't "get" calculus even after they are done with it.

 

[GregGreen]

Originally posted by: Drakkon
they used just "as x approaches" and the epsilon and sigma were just part of the limit equation.

This is how I learned it in AP Calc AB -- didn't know there were more advanced terms, but I haven't taken math since then....

 

[Alone]

Nope, but I was taught how to spell definition.

 

[Brainonska511]

I learned the formal proof in Calculus last quarter. The whole epsilon/delta nonsense.

 

[Goosemaster]

Originally posted by: eakers
yes
and we also weren't allowed to do integrals until we learned the proof for the fundamental theory of calculus :thumbsdown:

I fvking hated that

so much algebra to simply some of those...the memories burn

 

[Imdmn04]

Yes, this should be the first chapter of Calculus I.

I don't know how the hell did they not teach you that.

 

[Random Variable]

Originally posted by: Brainonska511
I learned the formal proof in Calculus last quarter. The whole epsilon/delta nonsense.

Don't take real analysis. Epilson and delta pop up everywhere.

 

[FleshLight]

I like having to do things in 8 or 9 steps when I can just use the power rule..

 

[Brainonska511]

Originally posted by: Random Variable

Originally posted by: Brainonska511
I learned the formal proof in Calculus last quarter. The whole epsilon/delta nonsense.

Don't take real analysis. Epilson and delta pop up everywhere.

I wasn't planning on taking analysis. Just finishing up my one-variable calc sequence this Wednesday with the final, then taking a multi-variable calc (not proof-based) for a possible Chem major. If multi-variable is ridiculously hard for me, then I'll just stick with a biology major.

 

[Random Variable]

Originally posted by: Imdmn04
Yes, this should be the first chapter of Calculus I.

I don't know how the hell did they not teach you that.

Well, techhically you would have to know something about the topology of the real numbers before that would really make much sense.

 

[Goosemaster]

Originally posted by: FleshLight
I like having to do things in 8 or 9 steps when I can just use the power rule..

*tried to keep a straight face*

It actually puts the whole concept into perspective and helps you later on in higher level maths when you come back to them again*


*bursts out laughing*

 

[Aikouka]

Eh I don't remember AP Calc well and I tested out of Calc 1~.

 

[Triumph]

Something like lim x->0 of f(x+h) - f(x), all over (x+h), or something like that. Been a long time since I've taken a derivative of anything.

 

[George P Burdell]

I was taught much better in school than in college. Then again, I skipped Calc I and II in college and I can't remember what calc III was about.

 

[jman19]

Originally posted by: eakers
yes
and we also weren't allowed to do integrals until we learned the proof for the fundamental theory of calculus :thumbsdown:

LOL same here - it wasn't much fun solving relatively simple integrals using limits only... lots of writing involved :thumbsdown:

 

[jman19]

Originally posted by: Random Variable

Originally posted by: Imdmn04
Yes, this should be the first chapter of Calculus I.

I don't know how the hell did they not teach you that.

Well, techhically you would have to know something about the topology of the real numbers before that would really make much sense.

Maybe he read about it in that first chapter, but it was unlikely a thorough treatment of the material. The intro to topology in Rudin gives a nice amount of knowledge before diving in to differentiation and integration.

 

[Riverhound777]

Hell if I remember. I took calc 1 in High school and Calc 2 my first semester in college. 6 years later I can't even remember the derivative of X^2.

 

[Hyperlite]

Originally posted by: Riverhound777
Hell if I remember. I took calc 1 in High school and Calc 2 my first semester in college. 6 years later I can't even remember the derivative of X^2.

2X


and i am hating calc 1 right now. Our prof is a grad student who is absolutely horrible at conveying anything. The class average on our first test (100+ people) was a 25/100. I Plan on taking Calc 2 over the summer and going straight to calc 3 in the fall. i figured i may as well do them all in a row....