Prerequisites for Electromagnetism?

[PieceOfPi]

Hi,

Just out of curiosity, what should I know if I am going to take upper-division electromagnetism course. The text for the course is Griffiths' Introduction to Electrodynamics. I am not a physics major (I am a math major), but I have taken the first-year, calc-based physics sequence, introductory differential equations, multivariable calculus (including some vector analysis), and linear algebra (both introductory one and abstract one). The only reason I'm even considering taking this course is because the subject sounds interesting (EM was one of my favorite subjects when I took the first-year physics), and it might contain some interesting applications of mathematics, so feel free to post your honest opinion.

Thanks

 

[maverick_starstrider]

Hi,

Just out of curiosity, what should I know if I am going to take upper-division electromagnetism course. The text for the course is Griffiths' Introduction to Electrodynamics. I am not a physics major (I am a math major), but I have taken the first-year, calc-based physics sequence, introductory differential equations, multivariable calculus (including some vector analysis), and linear algebra (both introductory one and abstract one). The only reason I'm even considering taking this course is because the subject sounds interesting (EM was one of my favorite subjects when I took the first-year physics), and it might contain some interesting applications of mathematics, so feel free to post your honest opinion.

Thanks

I'd say the ONLY prereq is a firm understanding of vector calc (and special functions/PDE's will help). On the physics side it's pretty much all in the book.

 

[PieceOfPi]

I'd say the ONLY prereq is a firm understanding of vector calc (and special functions/PDE's will help). On the physics side it's pretty much all in the book.

Thanks. What are the "special functions" that you've mentioned?

 

[maverick_starstrider]

Thanks. What are the "special functions" that you've mentioned?

There are certain PDE's that pop-up again and again in certain problems that have complicated but well studied solutions which are called "special functions". Examples are legendre polynomials, laguerre polynomials, hermite (polynomials), bessel functions, beta functions, gamma functions, etc. I don't think these will be of huge importance at griffith's level (although he does discuss legendre polynomials in a few places) but at a higher level they pop up a lot. (in general whenever you're solving certain equations (like laplace's equation) with certain symmetries)

 

[jtbell]

what should I know if I am going to take upper-division electromagnetism course.

What does your college's catalog list as the prerequisistes for the course?

 

[PieceOfPi]

What does your college's catalog list as the prerequisistes for the course?

It looks like the prerequisite is just vector calculus. I'm just wondering if this is enough to take this course, since I always feel like there is an "implicit" requirement in upper-division math/science courses.

 

[maverick_starstrider]

It looks like the prerequisite is just vector calculus. I'm just wondering if this is enough to take this course, since I always feel like there is an "implicit" requirement in upper-division math/science courses.

If there is no previous electricity and magnetism course as prereq (other than first year physics) then I'd say there isn't. They'll walk you through coloumb's law to biot-savart to maxwell's equations.

 

[jtbell]

It looks like the prerequisite is just vector calculus.

Not even the first-year physics course? But you've had that, anyway.

 

[PieceOfPi]

Not even the first-year physics course? But you've had that, anyway.

Nope, but I believe the most of the students who take this course are physics majors, so they have taken the first and the second year physics sequences already.

 

[Klockan3]

I would say that it is probably good for you to do it, but be aware that this course needs you to be able to understand the translations between maths and physics really well. If you can do it, then it is a piece of cake. But most are really bad at that so be prepared to work a lot for it.

I would say that the most important thing for you to know before the course that you might not know yet is this:
http://en.wikipedia.org/wiki/Gauss's_law

 

[PieceOfPi]

I would say that it is probably good for you to do it, but be aware that this course needs you to be able to understand the translations between maths and physics really well. If you can do it, then it is a piece of cake. But most are really bad at that so be prepared to work a lot for it.

Yeah, that might be a little difficult, since I didn't really use that much math beyond calculus in the first-year physics course (e.g. no vector calculus at all). I actually checked out Griffiths' text from the library so that I can read the first few chapters of it, and that might help me figure out how well I can translate between math and physics.

I would say that the most important thing for you to know before the course that you might not know yet is this:
http://en.wikipedia.org/wiki/Gauss's_law

Well, I guess it's a good news that I learned this in the first-year physics. :) But I'm willing to review it if that's really important, and my class didn't do anything with the differential form of this, so I might try and study it on my own.

 

[Klockan3]

Well, I guess it's a good news that I learned this in the first-year physics. :) But I'm willing to review it if that's really important, and my class didn't do anything with the differential form of this, so I might try and study it on my own.

Well, I guess that if you have already done that and also got all the maths then you got all the prerequisites for a griffits based EM course.

Also the reason you need to understand gauss law fully is because most of the statics in the EM course is about understanding how to place your gauss surface to make the problem solvable.

Lastly, I just recalled, is that in physics you often do a lot of unmathematical formulas with the justification "If these conditions are met the error becomes extremely small". A large part of physics is therefore understanding each formulas limitation so you can know where you can apply it and where you need to look into it with exacter ones.

So often you can't solve a problem using an exact formula, in these cases you should use one of the simplifications which fits into this situation. Many with a maths background have a problem with that. But at least in EM you don't got much of that at all, but it is still present in the form of dipoles and materials with zero resistance etc.

 

[PieceOfPi]

Well, I guess that if you have already done that and also got all the maths then you got all the prerequisites for a griffits based EM course.

Also the reason you need to understand gauss law fully is because most of the statics in the EM course is about understanding how to place your gauss surface to make the problem solvable.

Lastly, I just recalled, is that in physics you often do a lot of unmathematical formulas with the justification "If these conditions are met the error becomes extremely small". A large part of physics is therefore understanding each formulas limitation so you can know where you can apply it and where you need to look into it with exacter ones.

So often you can't solve a problem using an exact formula, in these cases you should use one of the simplifications which fits into this situation. Many with a maths background have a problem with that. But at least in EM you don't got much of that at all, but it is still present in the form of dipoles etc.

Thanks for your comments.

Yeah, I do remember back in first-year physics when we discussed things like "sin(x) is approximately equals to x" if x is "small enough," and used that type of approximation in order to justify formulas, and that certainly did annoyed me when I first learned it. I don't know if this is the same type of simplification you're talking about, but hopefully I can get used to it if I'm actually going to take the course.

 

[Klockan3]

Thanks for your comments.

Yeah, I do remember back in first-year physics when we discussed things like "sin(x) is approximately equals to x" if x is "small enough," and used that type of approximation in order to justify formulas, and that certainly did annoyed me when I first learned it. I don't know if this is the same type of simplification you're talking about, but hopefully I can get used to it if I'm actually going to take the course.

Well, the logic of it all gets much easier if you understand how each formula is derived.

Like your example, as long as the angle is small that is a very good approximation but if you get a problem with a large angle then you can no longer rely on that formula. So by knowing how the formula was derived you also know the magnitude of the error and if it is positive or negative.

After that all you need to figure out is how small the error should be for you to be allowed to use the formula, and that you need to ask your prof about if you take the course. Usually though it is quite obvious with the error either being less than ~1% or more than ~25%.

Edit: Also being able to derive the formulas makes the courses that much more rewarding.

 

[maverick_starstrider]

Thanks for your comments.

Yeah, I do remember back in first-year physics when we discussed things like "sin(x) is approximately equals to x" if x is "small enough," and used that type of approximation in order to justify formulas, and that certainly did annoyed me when I first learned it. I don't know if this is the same type of simplification you're talking about, but hopefully I can get used to it if I'm actually going to take the course.

Well ya, it's just the leading term of a power series expansion. Often when something is insoluble in physics we just expand in a power series and get a sense of how quickly the terms get small and discard higher order terms and work with that. In the case of sin(x) the second term is of the order x^3 so if x is small it will be small indeed.