Most Pertinent Topics; Calc 2 -> 3

[apt403]

Most Pertinent Topics; Calc 2 --> 3

Heyo,

Posted here a while back looking for books, as I was planning to study over spring and summer before I registered at a CC. Now it's time to pick my classes for my first semester.

So, I was wondering which topics in calc II I should be reviewing before I take calc III.

Calc II bored me, because it was like calculus I with a good deal of trig. and harder integration problems, so I decided to try my hand at linear algebra instead of calc III.

 

[novop]

I'd focus mainly on reviewing parametric surfaces, double and triple integrals, and elementary vector calculus (arc length, curvature...). Also 3D coordinate systems such as cylindrical and spherical are pretty useful in Calc III. Series and sequences don't make much of an appearance. I also agree about Calc II being somewhat boring. I think you'll enjoy Calc III a lot more.

 

[Jack21222]

There isn't much that carried over from my Calc 2 to Calc 3, but every school will be slightly different. At my school, Calc 3 was basically an extension of Calc 1 into 3 dimensions plus vectors.

 

[gretun]

These topics are very important

- Polar coordinates, but doing it in double/triple integral is much easier.
- Parametric equations, can be very helpful in line integrals
- L'hopital's rule can come in handy with limits for vector functions (but most instructors don't go over it)
- Integrals in general, just area, don't worry about rotation volumes
- Nothing on series/seque is in calc III, take a deep breathe
- Perhaps work on function transformations? Contour plot sketches are common

All I can think of. Calc III isn't that hard, but some instructors will deliberately make it difficult

 

[apt403]

Alright, thanks you guys. You've put my worries at ease. Series and sequences were what I was most worried about. I need to review L'Hopital's rule, and probably some of the integration techniques (I zone hard when I'm just doing a bunch of algebra in leibniz notation...)

I'm pretty disappointed in the number of math courses offered at this CC, Calc III is split into 4A and 4B, which'll keep my occupied for two semesters... And that's about it. I was thinking about taking finite mathematics, but after I looked at the syllabus, I'm worried I'll just be learning how to +-/x matrices. Everything else is rudimentary. I won't be taking calc-based physics until spring because of a spring/fall rotation they've got going for sequence classes, so that'll keep my busy, but I feel I'll have to take my mathematical education into my own hands.

 

[gretun]

Alright, thanks you guys. You've put my worries at ease. Series and sequences were what I was most worried about. I need to review L'Hopital's rule, and probably some of the integration techniques (I zone hard when I'm just doing a bunch of algebra in leibniz notation...)

I'm pretty disappointed in the number of math courses offered at this CC, Calc III is split into 4A and 4B, which'll keep my occupied for two semesters... And that's about it. I was thinking about taking finite mathematics, but after I looked at the syllabus, I'm worried I'll just be learning how to +-/x matrices. Everything else is rudimentary. I won't be taking calc-based physics until spring because of a spring/fall rotation they've got going for sequence classes, so that'll keep my busy, but I feel I'll have to take my mathematical education into my own hands.

I almost forgot now that you just reminded me, don't forget differentials...serious..they spent like a unit on it (or two when they extend it to gradient stuff)

 

[deadkitty]

Hmm that's odd nobody had much series and sequences. I just finished calc III at my school and over the 8 summer weeks, 5 weeks was series and sequences, and the last three were linear algebra/vectors. We covered all the series/sequence tests, taylor series,polynomial series conversions, and did a section on Fourier series. The L.A. stuff was mostly the basics, linear transforms, dot product, cross product, inverses, and determinants.

 

[Jack21222]

Hmm that's odd nobody had much series and sequences. I just finished calc III at my school and over the 8 summer weeks, 5 weeks was series and sequences, and the last three were linear algebra/vectors. We covered all the series/sequence tests, taylor series,polynomial series conversions, and did a section on Fourier series. The L.A. stuff was mostly the basics, linear transforms, dot product, cross product, inverses, and determinants.

When did you fit in the time to learn volume integrals, div, grad, curl, directional derivatives and the like?

 

[deadkitty]

Well, we covered volume integrals in calc II, and the rest of those topics are covered in vector calc A/B. 2 classes I have yet to take.

 

[Jack21222]

Well, we covered volume integrals in calc II, and the rest of those topics are covered in vector calc A/B. 2 classes I have yet to take.

I've never heard of such a class. That's a completely different system than I'm used to. By volume integrals, I don't mean the disk and shell method, by the way. I mean double and triple integrals, used to integrate a function OVER a volume.

 

[deadkitty]

Interesting,
my proggression was
calc I- differential
calc II- integral
calc III- series/sequence & intro L.A.
Then calc IV (multi-variable) is broken down into two classes vector A and vector B.

I guess different schools do it different ways.

 

[thrill3rnit3]

Interesting,
my proggression was
calc I- differential
calc II- integral
calc III- series/sequence & intro L.A.
Then calc IV (multi-variable) is broken down into two classes vector A and vector B.

I guess different schools do it different ways.

Are you guys in a quarter system?

 

[Jack21222]

The way I've usually seen it, with minor variations, is this:

Calc 1: Limits, Differentiation, basic integration

Calc 2: Advanced integration techniques, sequence and series, polar coordinates, intro to basic differential equations.

Calc 3: Vector algebra, planes, space curves, partial derivatives, multiple integrals, intro to vector calc (div, grad, curl)

Then there iswhat my school calls "advanced calc" which I haven't taken yet, but it goes more deeply into things like green's theorem and calculus of variations.

 

[deadkitty]

Yes we are on the quarter system. It seems, in the end, we all eventually cover the same things. So I would say just read the class description to find out what lays ahead.