calc 1 vs calc 2 vs calc 3

[evank15]

I thought calc 2 was the easiest..calc 3 was a bitch. but that might have had something to do with my fob from africa prof.

i hate math. in fact i hate school.

[T50_Omaha8]

I think most of the responses are biased towards how the professors were. Calc II is probably more often a weedout class, so it might be more difficult. Conceptually, they get more and more rigorous.

I never took calc III, but my registration software screwed up and let me take classes that required it as a prereq anyways, so I kind of had to pick it up. The parts of it I learned were pretty neat, and crucial for understanding probability theory.

[recipro]

For me, Calc 1 was most difficult, as I didn't take any calc in high school. After Calc 1, they got progressively easier, until Partial Differential Equations was simple as pie and I barely had to come to class.

[Wyman]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Calc II was the hardest for me but unlike you guys I found series and sequences to be the easiest part of the class. I had trouble with some of the integral stuff.

Edit:
This is off track but I need to take one more elective after the upcoming semester to complete my math minor and I was wondering what classes use the series stuff. I thought the Calc II stuff was kind of interesting but I don't know if there are any classes that specialize in that kind of stuff.

Maybe Real Analysis?

[/ QUOTE ]

Yes. A course in real analysis will spend a great deal of time covering sequences / series. Typically real analysis is one of the tougher undergraduate math courses.

What's your major?

[/ QUOTE ]
I'm a chem major. If Real Analysis is a really difficult class I'm staying away from it because I've already got enough [censored] on the chem side to worry about. I just figured that since I breezed through the sequence/series stuff in Calc II that a class focusing on them wouldn't be too difficult.

[/ QUOTE ]

As a chem major, stay away from real analysis if you're not looking for a challenge. More applicable to chem (and still related to some things you've seen in math) are differential equations and linear algebra.

[Wyman]

PS - Everyone who says Calc 2 is all memorization needs to take a better Calc 2 class.

[AceLuby]

[ QUOTE ]
PS - Everyone who says Calc 2 is all memorization needs to take a better Calc 2 class.

[/ QUOTE ]

How do you figure? Everything except series I learned in HS calc 1 and there are very few 'concepts' in series, just which series match up to what.

[thedustbustr]

[ QUOTE ]
PS - Everyone who says Calc 2 is all memorization needs to take a better Calc 2 class.

[/ QUOTE ]
go read a calc 2 syllabus and come back

[Wyman]

[ QUOTE ]
[ QUOTE ]
PS - Everyone who says Calc 2 is all memorization needs to take a better Calc 2 class.

[/ QUOTE ]

How do you figure? Everything except series I learned in HS calc 1 and there are very few 'concepts' in series, just which series match up to what.

[/ QUOTE ]

First, it's sort of unfair to describe a calc 2 class based on what *you* did in calc 1. If you took calc 1 in HS, you had a full HS year (which is longer than 2 college semesters) to learn it, whereas in college you only get 14 weeks.

Second, assuming calc 2 is all series (as it sounds like it was for you), I still claim that it shouldn't be all memorization. Your description "which series match up to what" sounds like you didn't have a very thorough introduction to series (I don't want to presume, though. It could just be that it's been awhile).

<boring mathy stuff>
Series are interesting for a few reasons. First, let's take Taylor series. How do you compute arctan(0.896)? The easy answer is "you put it in your calculator". How does the calculator do it? How did people compute these things 150 years ago? Well, one way to do it is to approximate arctan on an interval by a polynomial, ie computing a truncation of a Taylor series, and evaluate this polynomial (which is easy) at 0.896. Not only is it interesting that this does work, how one discovers or proves that one can compute a Taylor series is interesting.

But it's not just Taylor series. Series in general. You learn techniques to show that when you add up infinitely many things, they actually sum to something finite. And often you can say what that something is. Or you can show definitively (even as a calc 2 student), that the series doesn't converge.

All of the series tests are covered under "techniques". Memorizing them does not help you figure out which to apply for a given series.

Power series enable you to do some tough integrations.

In a good class, you might see applications of series to differential equations.
</boring mathy stuff>

A good understanding of series goes far beyond memorization. Add to that all of the applications of integration to physics and volume, as well as the techniques of integration (again, memorizing these does not teach you how to pick out which technique to apply), and calc 2 is a pretty amazing class.

It was my favorite. I'm also biased since I'm (hopefully) teaching it this semester, but I can assure you that my class will require thought, not just memorization.

[Wyman]

[ QUOTE ]
[ QUOTE ]
PS - Everyone who says Calc 2 is all memorization needs to take a better Calc 2 class.

[/ QUOTE ]
go read a calc 2 syllabus and come back

[/ QUOTE ]

I teach; I am fairly familiar with the syllabus. The syllabus is broad enough that you can have different levels of calc 2 classes.

Let me be clear. You can have really crappy classes where you get by with memorization. In fact, even in a decent class, you may be able to get by simply by memorizing some things (this is true in most intro classes in most departments at most schools). But if you have the right professor/school, it can be a really interesting class, and you can actually learn things well enough to be able to apply them later in physics, chem, engineering, architecture, whatever. You can (and hopefully will) understand things beyond the memorization.

[thedustbustr]

post got tldr; in a nutshell, "techniques" =/= "concepts". calc 2 is techniques. calc 1 and calc 3 and deq are concepts. u substitution is not a concept. integrating to calculate a velocity is a concept.



I teach too - I was a university paid math tutor for the last three years. I work with smart kids who did the homework and got stuck on a few problems, and I work with dumb kids, too - the ones who hate their teachers because they are always teaching at a way higher level than the non math/egr students are capable of understanding.

[ QUOTE ]

All of the series tests are covered under "techniques". Memorizing them does not help you figure out which to apply for a given series.

[/ QUOTE ]
er, by far the most common approach for any kid to get through this class is to memorize the 'techniques', and then memorize the little chart that tells you what goes with what.

Same with integration techniques, the core material of calc 2 - the only technique that actually doesn't require rote application of a memorized algorithm is u substitution.

http://www.rit.edu/~mkbsma/calculus/.../integral.html

Every single one of the linked techniques, other than u substitution, is not intuitive to anyone but a math professor or nerd who cares way too much and goes and derives them himself. I tutor the stuff and every year I have to pull out the text when some kid comes in with one of these problems, so I can learn how to do it again. For comparison, some kid comes in with a system of springs, its all still right there, because its intuitive.

Trig substitution? Simpson's rule? Integration by powers of sins and consines? not concepts, not intuitive, rote memorization.

I hope to god everyone's calc professors allowed a cheat sheet, because you have to know all this nonsense

[ QUOTE ]
A good understanding of series goes far beyond memorization. Add to that all of the applications of integration to physics and volume, as well as the techniques of integration (again, memorizing these does not teach you how to pick out which technique to apply), and calc 2 is a pretty amazing class.

[/ QUOTE ]
I hope you do have time to cover lots of integration application, and stay away from the wretched techniques.