Why do the collegeboard offer Electricity and Magnetism?

[khalkash]

If a prerequisite for E&M is Multivariable calculus, why is it offered in high school (without that pre-req)? Is the High School E&M equivalent to physics 2 in college, and if that is so, Physics 2 is still offered before Multivariate calculus. Can someone clear this up for me. Am I getting two different courses confused all together? I will be taking Physics AP next year, but I am very nervous about it as I am taking my first Calculus course along with it as well (BC).

 

[jtbell]

Multivariable calculus is pre-requisite for an E&M course above the introductory level, using a textbook such as Griffiths. This is a different course, at a more advanced level, than the second semester of a typical university introductory physics course (which AP Physics in high school is supposed to be equivalent to).

 

[lurflurf]

The ap physics requires only basic calculus. Strictly speaking there are a few things not ap in calculus that are useful and a full course in multivariable calculus would not hurt, these things can be covered in a few lectures in the physics class. Calculus the year before or concurrent is plenty and some people have even less. College courses vary, a few used multivariable calculus extensively and many use a little, but few focus on it.

 

[thegreenlaser]

Electromagnetics is a pretty tough nut to crack, at least in my experience, because it's one of the most math-heavy things you'll see at a high-school/undergrad level. The good news is, though, that you wouldn't jump right into the vector calculus. It seems that you pretty much learn E&M by making a bunch of passes over it, each time making it more in-depth and getting more involved with the math. A first pass, like you would see in high school, might not use any calculus at all. The focus would just be to try to familiarize you with concepts like charge, current, electric and magnetic fields, etc. You'll probably mostly see specific examples where they give you the formula for the electric/magnetic field rather than any of the general laws governing charges currents and electromagnetic fields. Even after a high school level exposure, you'll probably see another college-level E&M course (probably based on single-variable calculus) before you jump into the real meat of the theory with vector calculus.

So don't worry about it too much. Third year physics and electrical engineering students have a hard enough time making sense of the vector calculus they see in their E&M courses that it would be ludicrous to try to make a vector calculus-based high school course for people who have just seen calculus for the first time.

 

[hsetennis]

Although I did not in high school, some of my classmates took AP Physics C concurrently with AP Calculus BC. It's not easy by any means, but it's doable. By the time you start E&M, it'll be around December/January, and you will have already covered most of the calculus necessary. This is assuming you're taking Mechanics and E&M in one year, not two.

 

[khalkash]

I am going to put my full effort in my first physics course ever. But I am ambivalent (am I using this word right?) in whether I should use my AP credits (if accepted) towards my decided major (most likely physics, if not Applied Physics). I have read many threads on if you should use credits towards your major and the battle is 50/50. I want to LEARN physics, but I also would like to get ahead of the game. Any experiences here on this? Maybe I am just being too naive in trying to get ahead, perhaps slowing down might be the best. I still have a year to decide atleast.

 

[WannabeNewton]

I personally would take AP Physics C EM but only use the credit if your future university does not offer an honors introductory EM course. Don't worry about the math though because in my opinion the math in AP Physics C EM is quite elementary; it's just the physics you have to really focus on.

 

[khalkash]

I certainly hope so WannabeNewton, many teachers rolled their eyes when I said I am going to jump to BC from Precalc (not usually done), and especially because I have big gaps in mathematics. While their perspectives are discouraging, I am working my fullest throughout the summer to fill those gaps. And I mainly just have to thanks physics-forums for hearing many great stories similar to mine to give me motivation. Thanks for your help.

 

[WannabeNewton]

In my HS there were many people who went straight from honors trig/algebra 2 to calc AB/BC including me. There were also many people who went from precalc to calc AB/BC. Ay my HS there was a calculus placement exam to take BC in the first place so they didn't really care what exact level you were in school as long as you knew all the stuff necessary to start BC. My point is, don't let people discourage you or intimidate you; if you prepare yourself over the summer you will do just fine as long as you put as much effort as you can into homework. Best of luck.

 

[serllus reuel]

Regarding the original question: I just did Physics C EM and the math is, well, sort of funny. You won't use most of the more advanced stuff in BC (polar coordinates, taylor series, etc) but there is a bit of vector calculus in there. The math can get confusing, but only because it is new to the student. Sometimes it is the notation that is confusing! For example, I spent about five hours staring at a few pages of a physics book trying to make head or tails of Gauss's law because at the time I had no idea what a surface integral was. If you have the time and interest, skim through a multivariate calculus book before/during your study of E&M. You only need the basic concepts.

 

[jtbell]

At many/most colleges, the "normal" physics major course sequence has freshmen taking calculus-based introductory physics at the same time as Calculus I and II. The "normal" student taking the second semester of intro physics (E&M) has not yet taken Calculus III (multivariable calculus).

Intro physics courses usually introduces the concepts of line, surface and volume integrals in a pictorial / geometrical / conceptual manner. You evaluate them only in very symmetric situations where you can pretty much evaluate the integral by inspection of the geometry, rather than working out a full-blown integral like you would in Calculus III. I call them "Geico integrals:" so easy a caveman can do them.

 

[serllus reuel]

Intro physics courses usually introduces the concepts of line, surface and volume integrals in a pictorial / geometrical / conceptual manner. You evaluate them only in very symmetric situations where you can pretty much evaluate the integral by inspection of the geometry, rather than working out a full-blown integral like you would in Calculus III. I call them "Geico integrals:" so easy a caveman can do them.

That is correct. It seems easy to you, and it seems easy to me now, but I'm not kidding about the five hours on Gauss's law. Sometimes the difficulty comes from trying to utilize a mathematical concept when you have no idea of the theory behind it. Add the fact that authors of intro textbooks throw at he reader notations that they likely have never seen before. Personally, I think that physics is easier with more math, some author (I don't recall which one) said in a preface that doing physics with little math is like digging with a screwdriver. Learn to use a shovel, even if the hole you need to dig is small.

 

[jtbell]

I agree; I'm not trying to minimize the initial conceptual difficulties of surface integrals, as in Gauss's Law which is where I think most physics students first see them (in physics). At least they're not also struggling with the mathematical machinery of evaluating surface integrals using Calculus III techniques, which is why Calc III isn't a prerequisite for this.

 

[serllus reuel]

Well you are right in many ways, but when I first learned vector calculus (after intro E&M), I found myself several times going like,"Well THAT's what Mr [Giancolli, Serway, Halliday, insert name of author] was trying to say!"

 

[WannabeNewton]

There are introductory EM texts that introduce all the necessary math for EM to be studied properly (i.e. vector calculus). Purcell's EM text for example does just that and is intended for first year students; it is used in honors introductory EM courses at various unis. This is why I said if the OP's future university offers honors EM, then it would be worthwhile taking it if desired.