Preparing for Multivariable Calculus

[Char. Limit]

Well, I have a week and a half until my first classes in my first year of college. My math class is multivariable calculus. However, while I aced Calculus in high school, I'm worried that college-level may be of a different caliber. So, I wanted to ask what should I know walking into that classroom? I know there's something called Stokes' Theorem, should I learn that? Is there anything?

I was also wondering if you could give me some post-Calc II, pre-Calc III questions to refresh my mind. Any help would be greatly appreciated, as I'm slightly unnerved about college-level mathematics.

I guess this isn't quite a homework question, is it?

 

[sponsoredwalk]

www.khanacademy.org

The videos on multivariable calc would give you an idea of what to expect but are by no means complete

 

[Ouabache]

I've found college Calc courses to be a considerable step up from high school math. If you are really concerned, you might consider overlapping by taking Calc. II at college before jumping into multivariable Calc. I found multivariable calculus to be fairly straight forward, a natural extension of the concepts learned in single and two-variable calculus.

If you already have your heart set on taking Calc III in your 1st semester freshman year, I would review material toward the end of your Calc II text. Also try to find the Calc III syllabus on your college website. It should outline topics you will cover. If you cannot find one there, try math dept websites at some other colleges.

 

[yungman]

I never took Calculus in HS, but you are going to need the first two cal. class. Unless you are very very good in your class, I would enroll in the first two classes first. If you think you are that good, take both Cal I and II at the same time and see how you fair. The foundation is very very important. I was goofing off in my college days and not doing very well in Calculus, I have to re study the first two classes on my own before I go into Calculus III ( multi var). Or else you might miss out a lot of thing even though you might pass the multi variables. Passing a class is easy, problem is if you miss out something, it just get harder when you go to the advanced level. This is part of what I am struggling now.

As I said, I rushed through the first two. Even though I did very well in multi var and ODE and PDE, I often find myself got hung up on something that when I asked here, people were surprised I don't know that to be in the level I am in! That is not good. I am still trying to fill those holes. Don't get me wrong, I was the first in the ODE class, it just sometime when I asked a question in the class, the instructor and students kind of looking at me like " where have you been!"

Multi variable is not that hard. But if you go into ODE and PDE, you really need the first two classes. I cannot imagine your HS calculus can be anything close.

 

[vela]

Assuming you covered the all the material at the appropriate level of difficulty, I'd say your main adjustment will just be getting used to how college courses are taught. The pace will be a bit faster, and you'll be expected to take a more active role in your own education.

You should be fluent in algebra and trig by now. You should know how to take limits and know why a limit wouldn't exist. You should have a solid grasp of differentiation and integration. Since you'll be working in more than one dimension, being able to sketch functions will at times help tremendously in visualizing what you're calculating.

 

[benorin]

I have taught High school AP Calc AB & BC in addition to college level calculus sequence (including multivariable calc): if you passed your AP exams (recently, that is), and you feel you understand/can do harder problems in the following single variable calculus subject areas: computation of limits (calculation using limit laws, practical just do the limit problems, and epsilon-delta proofs), continuity, differentiation (limit of difference quotient definition, product rule, quotient rule, chain rule, log, exponential, trig and inverse trig derivatives, implicit differentiation, equations of tangent/normal lines, rate of change [e.g. physics: velocity & acceleration problems], related rates, higher order derivatives [e.g. 2nd derivative, 3rd derivative, ..., nth derivative], minimization/maximization problems, curve sketching [critical points, infection points, intervals of increase/decrease, concavity, local and absolute max/min, intercepts--the works], ...

Integration [Riemann sums, anti-derivatives, U substitution, integration by parts, integration in polar coordinates (limited), volume by cylindrical shells, volume by washers, etc...

you should be fine.

I recommend the $16 book Schaum's Outline of Advanced Calculus, 3rd edition by M. Speigel. Excellent, covers all the material, cheap, has solved problems and solutions to exercises.