Seeking calculus related guidance

[Razzor7]

I'm trying to figure out which classes I will be taking for my freshmen year in college. The score I got on my AP Calc AB test places me in Calc 2, but looking at the course syllabus it seems like stuff I already know pretty well. However, the school strongly recommends that students who took only AP calc AB retake Calc 1, so they would very very strongly not recommend skipping calc 2.

Now, I also took Ap phys C. My scores place me out of the physics class I'm currently registered for, because the more advanced physics class I would be taking requires one to take calc 3 at the same time.

Here's what I'm wondering right now: if my AP Phys scores qualifies me for a class that uses calc 2 (assumes knowledge of calc 2) and I feel comfortable with the subjects listed on the course syllabus, is it possible that I am qualified to take calc 3? I know that this stuff probably differs university to university but any advice is appreciated.

P.S. the text used in Calc 2 is Early Transcendentals by Stewart, a used copy of which I have already ordered for summer perusal purposes. I'm working on some of the challenge problems on the book's website. Will these give me an accurate measure of my ability?

EDIT: I guess now that I think about it I really don't even have credit for calc 2 so this may not be possible, but I find it extremely odd that they give out physics credit for knowledge I allegedly do not have.

 

[colonelcrayon]

Not directly related, but you should definitely check out Gilbert Strang's fantastic calculus textbook, available as a free PDF from MIT. Google for it.

I just finished AP Calc AB and am self-studying from this book over the summer. It's amazing.

 

[Nabeshin]

If your calculus AB class is similar to the one I took, you probably covered all of differential calculus, and dabbled in integration (perhaps up to u-substitution, this is where my class stopped).

If that's the case, I recommend you do go ahead and take Calc II from your university (Retaking calc I is probably lost time for you. There's really not much to it unless it is a calc I course for math majors, with rigorous treatments of limits and the like. Other than that it will be almost completely review, with only perhaps a few snippets of things you haven't learned, not enough to justify a semester wasted though). The first ~50% of the Calc II class will likely be review (through integration techniques, like I mentioned), but the material covered on series, sequences, power series, and taylor series really is something you need to know.

On to the physics classes: Assuming you have a general knowledge of integration, the physics class that assumes calc II knowledge shouldn't be that difficult. If it's an E&M class which will be using vector calculus, then you do need to be concurrently enrolled in calc III.

But, it is completely possible for you to take calc II and calc III at the same time. The missing information from calc II (series) isn't really present in calc III. Definitely doable, and probably not bad considering you have a half semester of review in calc II, so if your university let's you, this may be an option you might consider looking into.

Cheers!

 

[symbolipoint]

Think carefully - How well do you still know Calculus today which you already studied? Let that be your guide.

 

[colonelcrayon]

If your calculus AB class is similar to the one I took, you probably covered all of differential calculus, and dabbled in integration (perhaps up to u-substitution, this is where my class stopped)

Are you serious? My class covered u-substitution long before the end of school and made it to integration by parts,

 

[Nabeshin]

Are you serious? My class covered u-substitution long before the end of school and made it to integration by parts,

You make it sound like integration by parts is a world apart from u-substitution. It's like the very next thing you learn, lol. Anyways, a quick look at the ap calculus ab website shows that only antidifferentiation techniques up to substitution are on the AP test. (We just watched movies the remaining month after the test, a good use of time!)

 

[Feldoh]

Typically a calculus 2 class covers:

Integration Methods (Substitution, integral form of chain rule, trig substitution, etc.)
Infinite Series (power series, taylor series, maclaurin series, lagrange error bound, taylor remainder theorem)
Tests of convergence (Radius of convergence, and all of the tests)
Intro to differential equations

I'm sure there's more that's just off the top of my head. If you're familiar with all of those subjects then I'd consider asking the department to test out of it.

As for physics did you take both mechanics and e&m? If so you'll realize that the integration needed is minimal and trivial. Also the use of vector calculus in the e&m portion is close to none, and is all done using highly symmetric objects.

Anything higher than those two in terms of physics classes would probably require differential equations.