Is anyone here fluent at explaining Calculus?

[sisq0kidd]

Received a D in my AP Calc class back in highschool, but earned a 5 on the AP test. The highest achieving student in my class was actually only one of three people to fail the AP test.

As someone mentioned earlier, it's a tricky subject. No amount of studying will overcome that hurdle of just not getting it. It really does have to just click one day. After it clicks though, I think you'll realize it's one of the easier math subjects. Discrete math is what kicked my ass later on.

 

[GodlessAstronomer]

As someone mentioned earlier, it's a tricky subject. No amount of studying will overcome that hurdle of just not getting it. It really does have to just click one day. After it clicks though, I think you'll realize it's one of the easier math subjects. Discrete math is what kicked my ass later on.

This is exactly what happened with me. I struggled and struggled with Calc, then one week everything just seemed to come together and I realised it wasn't all that hard. Then I got to my discrete math course and it seemed too easy to be true to begin with. Then it started getting more and more difficult to the point where I really struggled (although I passed with a pretty decent grade in the end).

Edit - I think one thing I really struggled with in discrete math was the shear volume of information in the source.

 

[40sTheme]

Wow, is everyone on this forum butthurting about Calculus?
Easiest math there is; the concepts are simple and they lead up to DiffEq which is probably the most useful thing you can learn for ANY science/engineering major.

Don't worry if you don't get limit crap. You'll understand derivation/related rates/etc. unless you're a total failure at math. If you hate proofs, get out of whatever major you're in because it's probably some form of science. If you're not willing to learn how stuff works, how are you going to improve it?

 

[TheLonelyPhoenix]

IIRC from my proofs class, the delta/epsilon thing said that given any range of values on the y-axis (the epsilon>0), you can find a corresponding range of values on the x-axis (the delta>0) for which all the function values fall inside the epsilon range.

If you remember the basic "definiton" of a limit you probably heard in your first calc class ever (the value of f(x) as x gets "really close" to some number) - its just a more descriptive way of saying the same thing. If you pick a range of values "close to" the limit, you can find some values on the x-axis to match up with them via f(x). That's it.

PM me if you have questions. Good luck.

 

[BlackTigers]

Thanks guys, and thanks Tenshodo. That link's pretty awesome.

And TLP, I understand what the two variables represent, it's just I struggle in determining what values I can use for "epsilion" to make "delta" true.

 

[TheLonelyPhoenix]

You can use any value you want for epsilon. The definition says that whatever positive number you pick for epsilon, however small, you can find some positive number delta to go with it.

 

[Matthiasa]

You can use any value you want for epsilon. The definition says that whatever positive number you pick for epsilon, however small, you can find some positive number delta to go with it.

Unless you pick a dumb spot and end up on an vertical asymptote.

 

[mrblotto]

Only calculus I know of is the kind the dentist scrapes away. I DONT wanna be fluent in that!

Gah! I just googled it..........OMG!

*runs away*

 

[TheLonelyPhoenix]

Unless you pick a dumb spot and end up on an vertical asymptote.

In this case, no matter what value of epsilon you choose, there is no value delta that will satisfy the condition. So yes, the definition means that there is no limit at a vertical asympote.

Edit: More precisely, there is no finite limit at a vertical asympote. There can still be an infinite limit, which IIRC has a different definition - I'd have to go dig up my old proofs text to be certain.

 

[nick1985]

Call this guy!
http://www.youtube.com/watch?v=EX_is9LzFSY

:biggrin:

I bet that guy gets a lot of pussy

 

[Sumguy]

Of all the calculus classes I've taken, I actually found calc 1 to suck the hardest. I passed with a C+ (my fault since I didn't go to discussion sections to take the quizzes), but I'd never take that course again.

The good news is, calc 2 teaches you to integrate like a boss with some sequences and series thrown in. I found it a lot more straight forward. Calc 3 introduces you to vector calculus and double/triple integration, which I guarantee you involves much less rape than you'd think.

Right now I'm taking differential equations. Definitely seems to be the most useful.

 

[Nik]

"You want to learn calculus? It's easy. First, remember all that stuff you learned in Algebra? Forget it. Here's a bunch of easier ways to solve the same problems."

 

[eLiu]

Holy shit guys, CalcI can never, ever be construed as "hard". It just doesn't happen. If you want to see hard, try (Real) Analysis I.

I never understood the teaching of epsilon-delta in calcI. In most cases, you don't prove anything useful with it. You just do some silly shit where you like verify that the limit as x->2 of 2*x is 4. Wow, yay. Introducing epsilon-delta seems to obscure the key concepts by burying them under intimidating mathematical notation.

OP: might be easier to help if you could post your current understanding of epsilon-delta limits. What's the definition? If I draw a picture of f(x), what does that definition mean graphically? Suppose I want to prove something obvious, like the limit as x->2 of f(x) = 2*x is 4. How would you try to do it? Maybe these things are all obvious/easy to you... my point is that it'd help us to understand what you don't understand.

 

[Matthiasa]

Holy shit guys, CalcI can never, ever be construed as "hard". It just doesn't happen. If you want to see hard, try (Real) Analysis I.

Eh few are saying calc 1 as a whole is hard, since its not unless someones really really bad at math.
Oh and nice comparing a 100 or 200 level class to a generally graduate level mathematics course.


Unrelated-(related to rest of topic)
Calc 1= easy
calc 2 = can be hard (typically a weed out class)
Calc 3= easier then calc 1
Differential equations 1=medium to easy if studying

 

[alkemyst]

I think more of the difficulty in Calc I is due to it being one of college's first experiences and many have more time management at that time.

Looking back almost my entire undergrad was really a cakewalk.

 

[BlackTigers]

Holy shit guys, CalcI can never, ever be construed as "hard". It just doesn't happen. If you want to see hard, try (Real) Analysis I.

I never understood the teaching of epsilon-delta in calcI. In most cases, you don't prove anything useful with it. You just do some silly shit where you like verify that the limit as x->2 of 2*x is 4. Wow, yay. Introducing epsilon-delta seems to obscure the key concepts by burying them under intimidating mathematical notation.

OP: might be easier to help if you could post your current understanding of epsilon-delta limits. What's the definition? If I draw a picture of f(x), what does that definition mean graphically? Suppose I want to prove something obvious, like the limit as x->2 of f(x) = 2*x is 4. How would you try to do it? Maybe these things are all obvious/easy to you... my point is that it'd help us to understand what you don't understand.

Sure, thanks.

Suppose I'm given a graph of f(x)= (5x-4), finding the limit as x approaches 2.

I could tell you the limit was 6.
I know that the epsilon is the range in y-values, corresponding to the delta change in x.

I could also tell you that the delta I would chose, for this problem, would be e/5. I got that from simplifying down the epsilon side until I got (x-2)<e/5. However, from there I am not sure what to do, as in how to prove it.

-------------------------------------------------------------
Given another problem: lim (x^2+x-11)=9 as x approaches 4.

I get the epsilon side down to |x+5||x-4|<e and 0<|x-4|<delta.

From here,
1) I need to get rid of the "X+5" on the epsilon inequality.
2) How do I prove it?

....fuck

 

[Merithynos]

I dropped Calculus I twice, since both times I ended up in classes with foreign professors with limited command of English. PSA: it doesn't matter how bright you are if you are incapable of communicating basic concepts in the language of your intended audience.

Took Discrete Math (somehow the Calc 2 pre-req didn't make it into the catalog) with a professor that didn't scrape by on the TOEFL and got an A. Never did go back and re-take Calc.

 

[AznAnarchy99]

Failed AP Calc in high school, failed Calc 1 in college. Now all my classes are poly sci.

 

[fatpat268]

Calc was easy overall. It took a little while for it to click for me as well, but I eventually got it.

I still don't understand to this day the epsilon delta definition. I mean, I understand the definition of a limit perfectly, but the epsilon delta definition seems too long winded to explain something that could be explain a lot more quickly.

 

[GodlessAstronomer]

Holy shit guys, CalcI can never, ever be construed as "hard". It just doesn't happen. If you want to see hard, try (Real) Analysis I.

Maybe not at your shitty school, but it seems most people here agree that Calc I is a very difficult subject.

 

[OBLAMA2009]

http://www.learnerstv.com/

i havent checked it out

 

[BlackTigers]

I ***THINK*** I'm starting to get it....so far.

http://i50.tinypic.com/25h2vk9.jpg
http://i48.tinypic.com/2zgvi2e.jpg

Do those look right? It just feels weird....I don't feel like I'm proving anything. Once I find the Delta, in terms of epsilon, I just seem to be retracing my steps to prove that I didn't make any mistakes...

Now I get to move on to doing them with constants introduced, and then infinite limits. Fuck.

 

[Schadenfroh]

Maybe not at your shitty school, but it seems most people here agree that Calc I is a very difficult subject.

I did not do well in Calc I, but I certainly did not fail. I made As in Calc II, III and IV. Depends on the teacher, I could make College Algebra a living hell if I wanted to torture undergrads. My Calculus I and II classes were mostly theory and proofs with very little actual problem solving, especially I.

Probably going to take the graduate advanced calculus next semester, that will probably be interesting. Either that or the graduate partial DE. I am knee deep in algorithms and multivariate statistics right now.

 

[DrPizza]

Maybe not at your shitty school, but it seems most people here agree that Calc I is a very difficult subject.

I've been teaching Calc I for 10 years. I've never had a student claim that it was harder than pre-calculus.

 

[Chaotic42]

Buy it, read it, love it.