Where does Calculus II pick up?

1. Aug 3, 2011

1MileCrash

August 22nd is my first day of school, I'll be taking Calc II. I'd like to prepare now.

It seems like Calculus I and II at any given school generally use the same textbook, my Calc I textbook was only covered about half-way in calc I. However, I'm transferring and it's no longer the same book.

The last thing I learned was integration and differentiation involving e powers and logarithms, u-substitution, etc. I took calculus I over the summer and just finished so a review is probably not necessary.

What should I learn in my 20 days before class for calculus II?

2. Aug 3, 2011

BloodyFrozen

Power series, taylor/maclaurin series+convergence, etc... Just check from a Calculus II Syllabus.

3. Aug 3, 2011

DrummingAtom

Calculus II picks up on MATH AWESOMENESS. Our first section was Numerical Integration, which blew my mind. Taylor series and convergence tests were also nuts. You're in for a fun class.

4. Aug 3, 2011

QuarkCharmer

I also just finished Calculus I last semester, and I started teaching myself Calculus II in preparation for the fall semester (I'm about 3/4 finished with it). While they do not go into great detail, I found that the videos on Khanacademy, starting with the first one after solids of revolution are basically in the order that my Calc II syllabus prescribes. I have been working through Khanacademy, watching the lectures on ocw.mit.edu (though it's hard to tell what is what because they have Calculus in 2 parts, instead of 3) and working through problems in Stewarts "Calculus" as well as Spivaks book of the same name.

I think if you watch the Khan Academy videos to get the general idea, then read that chapter of your book, and do a nice sample of problems you should progress through the subject easily. As mentioned above, the Taylor/Maclaran series is especially interesting leading up to eulers identity and such.

5. Aug 3, 2011

:rofl:

Well said!

6. Aug 3, 2011

Chunkysalsa

Really differs from school to school and class to class. From what I've see Calculus 2 generally covers integrations techniques, application of integrals, and series stuff.

7. Aug 3, 2011

Nano-Passion

We need a like button on the forum xD

8. Aug 4, 2011

romsofia

It should pick up on revolutions of solids/integration by parts. Like others have said, calculus two is a pretty fun course (other than trig substitution >.<).

9. Dec 10, 2011

1MileCrash

BUMP, that went well.

Now, who can tell me what I should do for Calc III this spring over the break?

10. Dec 10, 2011

AnthroMecha

11. Dec 10, 2011

If you'll allow me to hand-wave a bit ...

Calc III has been much more conceptual in nature. The techniques learned in the previous two courses haven't really changed: you'll certainly use all of them, though.

The hardest part for me was getting used to visualizing what a function is doing in 3-space, and then setting up the problem appropriately (choosing appropriate bounds of integration for double and triple integrals, and also recognizing when I should be using a different coordinate system). Everything that follows is simply taking partial derivatives, cross-products, evaluating integrals, things of that nature. Again, nothing you haven't done before, the setup is just different.

I'd review coordinate system conversions, basic operations with vectors, and conic sections (what they look like on a graph and how to recognize one by its equation). That should give you a good head start. If your integration techniques are solid, then the only hurdle should be the adjustment to working in 3-space, which might not be that big-a-deal depending on how your brain works.

12. Dec 10, 2011

victor.raum

Hey 1MileCrash, differentiate this series-based function if you dare:

$$f = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots + \frac{x^n}{n!}$$

Especially consider the case of n=$\infty$, or more precisely $\lim_{n \to \infty} f$

Everyone else: shh, don't give the fun away :-D

13. Dec 10, 2011

1MileCrash

That's just taylor series for e^x..