Alright, sci, I've been studying physics throughout highschool

>>8570718
I don't know, I've been taught the differential form first.

>>8570728
When you learned it, was it single variable or did you differentiate along x,y,z?

>>8570730
Our professor explained to us that Cartesians coordinates were not worth the hassle. We would always work in spherical coordinates, with symmetries and invariances so that only "r" would change.

So yes, it was single-variable in a way.

t. engineer

>>8570731
Liberal arts college really screwed me over on this one....

Alright thats another thing I have yet to get into. Im taking calc 3 next semester, is that my missing piece?

i think the integral forms are easier to compute initially (dl, E, ds etc usually come out as constants) and they give more of an insight into what's actually happening in specific problems

the differential forms give you more of an insight into the general nature of EM and also require more vector calculus

>>8570738
I don't know what "calc 3" is, sorry.
I'd say that it's vital to know how to switch from Cartesian to Spherical, it's vital to know how to derive the unitary vectors of Spherical coordinates. Having a good sense of geometry helps a lot, since there are symmetries everywhere.

As for calculus, you need to know how to do flux integrals and line integrals, plus a good deal of vector analysis, especially if you go into waves.

>>8570744
makes sense, when did the transition happen from one to the other? freshman/sophomore year?

>>8570750
So then do you use spherical coordinates for each law? Or just Guass's laws for electricity and magnetism?

>>8570767
Spherical coordinates for Electric field in electrostatic.
Cylindrical coordinates for Magnetic field in magnetostatic.

I took the class quite a long time ago, so I don't really remember what happens when you combine the two, sorry.

>>8570768
Ok gotcha, looks like I gotta study up before I get rekt. Thanks

quaternion is the only way to understand Maxwell's equations.
The inherent rotations and torques involved in magnetic field interactions require it

>>8570779
Isnt this just unit vectors and cross products?

Well, just look into the divergence theorem and stokes theorem and you'll see that the integral and differential form are the same. This is something you should be able to do in 2nd year of uni.

Start with some 2D vector calculus first, you'll need it to proof greens theorem, which you can use to proof stokes theorem.
Some topics:
- Vector fields, scalar fields
- Nabla operator (gradient, curl, divergence, ...)
- Vector identities and properties http://www.math.ubc.ca/~feldman/m317/vectorId.pdf
- Helmholtz decomposition of a vector field
- Line integrals
- Surface integrals
- Greens theorem
- Stokes theorem
- Volume integrals
- Divergence theorem
...

Maxwell equations are really beautiful when you understand the math behind them.

>>8570815
Basically this. It's worth it to derive the differential form yourself from the integral form and it is pretty easy as well. I really like Griffith's book. He builds these things from the ground up using the most basic experimental results.

>>8570718
Integral and differential forms are completely interchangeable. Somewhere in that book it should tell you exactly how to do it. You may not understand it at first, due to inexperience with multivariable/vector calc and stokes/divergence theorems. Just pick up a multivariable/vector calc textbook from the library and look up del identities (there's two in particular you will need), and the aforementioned theorems. After a good while, if you're not mathematically retarded (I'm assuming you're not by this stage), you will be bale to understand and change between them like it's second nature. Understanding them conceptually may be more challenging though, and you will need to do physics problems in order to get a better grasp. Remember, understanding always takes time and persistence, but you know dat orgasm feel when you conquer something that previously perplexed you. Keep at it, Anon.

>>8570768
Combine the two and use rectilinear I think.

>>8571016
Griffiths also has a chapter devoted to multivariable calculus that might be helpful.

>>8570768
That's because for time independent fields, electric fields are divergent (diverginging from a single point--spherical) and magnetic fields are divergenceless with curl (curling around a line makes a cylinder). Of course, there are plenty of charge and current distributions in which these won't be good choices.

We are able to see which coordinate system to use because we thought about the differential form.

>>8571082
Yeah, that was one of the few things I memorised.
The other is that electrical fields are "1/r^2" fields and magnetic fields are '"1/r".

>>8570718
>Why are we taught the integral form first

Because charged point particles necessitates the use of delta functions / distributions to describe them.

>>8570762
>freshman, sophomore, etc
you americants and your retard terms are so cute

It's the integral form that has physical meaning. The physical consept of a flux can be expressed mathematically using area integral.

>>8570738
If you don't know multivariable, you won't know vector calculus well enough to understand the way of transforming the integral form into the differential form.

>>8571450
If you begin with Coloumb's law and the principal of superposition, the integral form is the intermediate step to deriving the differential form. There is probably some way around that to get the differential form first, but it would be much more difficult.