How difficult is calculus to learn?

[Holocene]

Let's say that someone has a very good understanding of algebra.

How hard is it to transition to calc?

 

[dtl42]

Its not that hard, first time taking it, I had a good algebra base, and the only stuff I struggled the least bit with was Delta-Epsilon Definition of a limit. Its really fairly simple, so long as you have a good teacher and book, or a good discipline.

 

[dontdisturbmycircles]

The math involved in learning calculus is not hard at all, it's basically all just algebra and trig. Sure you can make it hard but for the most part it is not.

Learning calculus is hard in that it demands more effort to understand it. I think a big tip is to read actively, try to solve the example problems first before you read their solution etc.

 

[Invictious]

Calculus is a huge step taken from pre-calc.

No matter how simple or annoying pre-calc is, it is so important, I cannot stress this enough, without pre-calc, you can forget about calculus. It's the foundation of doing well in calculus. When I first learned calculus, I rushed through pre-calc, and of course I deeply regretted. I have to learn it all over again and it was a breeze the second time.

What I also found difficult about calculus was, obviously, the concepts. The limit definition, fundamental theorem of calculus, Riemann Sums etc etc, it takes time to truly understand it. You have to understand it inside out. Make sure there is not a little bit of uncertainty in the back of your mind, or it will grow and you will just...die..

 

[mathwonk]

most people think it was hard, but as sylvanus p. thompson said; what one fool can do, anoiher can.

so if I learned it, you definitely can. It helps if you grade it and then teach it a couple times. and it helps if youn use a good book, like courant, or spivak, or courant and john, or apostol.

 

[Romanian]

I will reiterate what other have said here: it's not hard at all. I took it my freshman year in high school, and it was a breeze. But then again, nothing is hard if you really try and want to do it.

 

[Holocene]

Great replies, thanks.

 

[mathwonk]

and a good algebra background is THE best prerequisite for calc.

 

[ice109]

Calculus is a huge step taken from pre-calc.

No matter how simple or annoying pre-calc is, it is so important, I cannot stress this enough, without pre-calc, you can forget about calculus. It's the foundation of doing well in calculus. When I first learned calculus, I rushed through pre-calc, and of course I deeply regretted. I have to learn it all over again and it was a breeze the second time.

What I also found difficult about calculus was, obviously, the concepts. The limit definition, fundamental theorem of calculus, Riemann Sums etc etc, it takes time to truly understand it. You have to understand it inside out. Make sure there is not a little bit of uncertainty in the back of your mind, or it will grow and you will just...die..

pre-calc for calc? maybe in knowing the shapes of the trig functions? i don't even remember what i learned in pre-calc but that means i didn't use much of it in calc.

seriously not that hard. if all the engineers and doctors and random people can learn it then it must be pretty easy cause most of the those people are pretty dumb

 

[DavidSmith]

the key to calculus is learning how to differentiate and integrate

note: the later is much more difficult

 

[ice109]

the key to calculus is learning how to differentiate and integrate

note: the later is much more difficult

all smooth continuous functions are differentialbe. there is no such theorem for integrals

 

[morphism]

all smooth continuous functions are differentialbe. there is no such theorem for integrals

?

By definition a smooth function has derivatives of all orders, so it's certainly differentiable. On the other hand, a continuous function is not necessarily differentiable. But a continuous function is integrable.

 

[ice109]

then i am extremely mistaken, its late I'm sorry

 

[proton]

the key to remember is that learning calculus will require much more effort than learning algebra, trig, and precalc.

I've always been good at algebra, but I had difficulty learning calculus at first since at the time I first learned it, I wasnt too motivated in learning

 

[leon1127]

?

By definition a smooth function has derivatives of all orders, so it's certainly differentiable. On the other hand, a continuous function is not necessarily differentiable. But a continuous function is integrable.

continuous function on compact interval. Should we even consider finitely many discontinuity?

 

[Bionerd]

Math has always been my toughest subject, but I've gotten better grades in calculus (Calculus in 10th grade, AP in 11th) than I have gotten for math in years. I took Pre-calculus in 9th grade and hated it to so much. There's been a few times where we've had to use what we learned from it, but I honestly don't believe it's necessary. If you have a strong knowledge of algebra and a good teacher, calc. should be no problem.

 

[Kurdt]

While developing a couple of calculus courses I think that the teaching or the approach to calculus is all important. Having done a couple of calculus courses with different approaches and then finding my favourite text on the subject, I can safely say that they can make the difference between it being very hard or very easy for you. So I would recommend having a good look at a few texts that use different approaches and see which one strikes you as the most appropriate for your understanding.

Having said that learning to differentiate and integrate is very easy. Depends if you want to understand what you're doing or not.