What's the Difference Between Calculus I and Calculus II?

[wScott]

What's the defference between Calculus I and Calculus II? I keep hearing them as separate terms and have no clue of the differences.

 

[JasonRox]

Calculus I is basically just teaching you the basics, and to start learning about integrals.

Calculus II is mostly applications of the integral. It also has an introduction to differential equations, power and taylor series, and maybe something else too. That's basically it though.

That is standard I think.

 

[wScott]

Thanks, Jason. I'm a little bit lazy at the moment as it it Friday over here, or I would look for it in the forums, but if you could tell me what an integral is, that'd be great.

 

[JasonRox]

The integral is like the anti-derivative.

http://en.wikipedia.org/wiki/Indefinite_integral

Read the first 3 paragraphs and you should get it.

 

[wScott]

Well, if I'm to understand what an integral is I better get my but in gear and try to understand a littlem ore than what I already know. I know not one of those two terms :(

 

[JasonRox]

Well, if I'm to understand what an integral is I better get my but in gear and try to understand a littlem ore than what I already know. I know not one of those two terms :(

Did you learn about derivatives?

If not, don't worry about it yet. You learn them in Calculus I, which is the whole purpose.

 

[wScott]

Ahh okay, well I'm going to finish my 3 years of pre calc next year than I'll be off to a year of Calc that I can get at my school, I get to even take the college calc exam to a hal or quarter of the price :)

 

[matt grime]

What's the defference between Calculus I and Calculus II? I keep hearing them as separate terms and have no clue of the differences.

that would heavily depend upon the country of origin, the level (school, university), and the individualy institution. no one can answer this question for you since we have no idea what they are.

 

[shmoe]

Jason's description is more or less standard for Canada (and the US I suppose), but it can vary as matt says. Check the course descriptions provided by your institution.

 

[Curious3141]

At what age do you learn all this ? In Singapore, we learn basic calculus, including differentials, integrals, calculation of areas under curve, volumes of solids of revolutions and simple first order d.e.s with separable variables at the age of 15-16 (secondary school). At 17-18 years of age, we cover further simple diff. equations (up to second order), Taylor/Maclaurin and other stuff to round off the knowledge.

I know that in India they do it at an even earlier age. I'm just curious as to what age calculus is introduced there in the US.

 

[shmoe]

In Canada it will vary by province but it's typical to have a first calculus course that covers derivatives and some basic integration in the last year of high school, ages 17-18 or so. It would be a stretch to say the average student who takes calculus at this level actually learns anything though, evidenced by the number of students entering university who believe it's possible "to understand derivatives but have no idea what a limit is". I've heard that a frightening number of times.

 

[cepheid]

At what age do you learn all this ? In Singapore, we learn basic calculus, including differentials, integrals, calculation of areas under curve, volumes of solids of revolutions and simple first order d.e.s with separable variables at the age of 15-16 (secondary school). At 17-18 years of age, we cover further simple diff. equations (up to second order), Taylor/Maclaurin and other stuff to round off the knowledge.

I know that in India they do it at an even earlier age. I'm just curious as to what age calculus is introduced there in the US.

I wish we had this sort of foundation in math. But as Schmoe said...nope. Oh well...

 

[pinkumbra]

I'm two years ahead of my math class and I'm only beginning Calculus next year (11th grade, I'll be 16-17). Virginia, United States.

AP Calculus AB is what I'm assuming you're taking, and then AP Calculus BC. Jason pretty much nailed the description, emphasis on diff. equations.

 

[finchie_88]

lol, over here in England, calculus is introduced at about 16-17 years old, but is then developed upon at 17-18 years old. Even then its quite basic. I think normal maths is a joke, I don't know how people fail. Anyway, there are not many universities that will take you on as a student to do physics and even fewer to do maths if you have only maths a-level. To do that kind of thing, most universities won't even consider you unless you have further maths on top, especially the better universities.

For normal maths, it starts by integrating polynomials (e.g. $$y = x^3 + 2x^2 +3$$), and then it carries on to integrating $$y = e^{kx}.or.y = x^{-1}$$, integration by parts, integration by substitution, etc. In further maths, it gets a little more advanced, and things like $$y = \frac{1}{\sqrt{9 - x^2}}$$. Power series expansions are also done.

I could go on, but I'm not going to.

 

[matt grime]

Sorry, finchie, but that is conplete rubbish. Single maths is all that the majority of universities require from their students for maths or physics degrees. In fact my guess is the totaly number of universities that demand further maths (for a maths degree) is fewer than 3 I think, and for physics it is no more than 1, if that.

What is true is that at say a place like Imperial, which doesn't require further maths is that they will not look kindly on people who were offered it but did not take it. However it is not absolute that you will not get a place, but entry is highly competitive and you will be at a disadvantage.

Also bear in mind that not everyone goes to a sixth form that has the ability to offer further maths.

 

[JasonRox]

Sorry, finchie, but that is conplete rubbish. Single maths is all that the majority of universities require from their students for maths or physics degrees. In fact my guess is the totaly number of universities that demand further maths (for a maths degree) is fewer than 3 I think, and for physics it is no more than 1, if that.

I've never seen a university ask for more around here.

They do recommend that you participate in math competitions though. Atleast once or twice.

 

[matt grime]

Jason, the systems of the UK and Canada do not compare at all.

 

[JasonRox]

Jason, the systems of the UK and Canada do not compare at all.

Yes I know and that is why I referred to Canada.

University of Waterloo doesn't expect more than basic knowledge, and they are reknown in the mathematics department. (You probably heard of them.)

Because of this, I find it unlikely that schools would demand more elsewhere. If it's very competitive, maybe.

 

[matt grime]

Sorry, I thought you were somehow trying to directly relate A-level to Canadian Highschool.

And yes, I know (people in) Waterloo Maths; you should perhaps consider doing some quantum mechanics.

 

[mathwonk]

to illustrate matt's point, at harvard in 1960, calc 1 (math major level) was axiomatic treatment of real numbers, infinite sequences and series, topology of the real line, (compactness, connectedness), differentiation, exponential and trig functions, Riemann integration, vector spaces, dot products and prehilbert and hilbert spaces, differential equations.

calc 2 was abstract development of finite dimensional affine spaces, infinite dimensional vector spaces, banach spaces, bounded linear functions and norms, quotient spaces, Hahn Banach theorem, derivatives of maps on Banach spaces, implicit and inverse function theorem, finite dimensional manifolds, content theory in finite dimensional Euclidean space, exterior algebras and determinants, and differential forms and their integrals on manifolds, including Stokes theorem, spectral theory of compoact hermitian operators, and applications to sturm liouville theory of differential equations.

(to the best of my memory.)

 

[cepheid]

to illustrate matt's point, at harvard in 1960, calc 1 (math major level) was axiomatic treatment of real numbers, infinite sequences and series, topology of the real line, (compactness, connectedness), differentiation, exponential and trig functions, Riemann integration, vector spaces, dot products and prehilbert and hilbert spaces, differential equations.

calc 2 was abstract development of finite dimensional affine spaces, infinite dimensional vector spaces, banach spaces, bounded linear functions and norms, quotient spaces, Hahn Banach theorem, derivatives of maps on Banach spaces, implicit and inverse function theorem, finite dimensional manifolds, content theory in finite dimensional Euclidean space, exterior algebras and determinants, and differential forms and their integrals on manifolds, including Stokes theorem, spectral theory of compoact hermitian operators, and applications to sturm liouville theory of differential equations.

(to the best of my memory.)

Holy ****. I could be wrong, because I have never studied real analysis, but it sounds like you are saying that first year calculus at Harvard in 1960 was just what is now called Real Analysis, i.e. build up knowledge of calculus from the basics with full rigour. But surely not for engineering students, etc...others studying more applied math?

 

[JasonRox]

Holy ****. I could be wrong, because I have never studied real analysis, but it sounds like you are saying that first year calculus at Harvard in 1960 was just what is now called Real Analysis, i.e. build up knowledge of calculus from the basics with full rigour. But surely not for engineering students, etc...others studying more applied math?

Yeah, it's basically Basic Analysis and Real Analysis what he described.

It's totally doable to do these classes right at the beginning. People make these courses sound like hell for some reason when they are not.