Never *really* learned vector analysis, should I self learn?

[colin.mcenroe]

Hello,

I am a physics major and just transferred to UC Davis from a community college. My multivariable calculus course did not for some reason include vector analysis even though it tranferred as such. In other words, the requirement is met, but I don't have the knowledge. I did audit a course last semester at my community college where the professor actually did teach this material, but I was so overloaded with other classes (19 units) that I did not have the time to study it (nor the motivation). Anyway, I am going to start my upper division courses in the fall quarter, so I have plenty of time to "relearn" the material and have it sink in. Is this something I should do now, or is it something I will pick up as I go?

Thanks for advice!

 

[marcusl]

Congratulations! UCD is a fine school.

My advice is to learn this material *thoroughly* now while you have time. There is a great deal of challenging information to master in upper division physics. If you struggle with material everyone else has down pat, they'll leave you behind on the new stuff.

If you have still more time, I suggest reading ahead as well for your upcoming courses. Difficult concepts in Quantum Mechanics, for instance, will be easier to grasp in class if you've seen them once before--even if the first time you don't fully understand them. Equally important, this will also allow you to pinpoint any other areas of lower division math or physics where your preparation needs augmentation.

Good luck!

 

[proton]

your situation sounds similar to my linear algebra/DE class I took at a community college last summer. Even though I got probably the highest grade in the class, I definitely didn't master the material. I kept thinking whether I should relearn everything I didn't understand or just hope that I learned enough to be prepared for my future classes. I eventually decided to self-study the linear algebra and DEs, and the 2nd time through, everything made perfect sense! My anxiety was relieved.

My advice is to follow what marcusl said. Relearn this stuff now while you have the time so you can enter your upper-div classes with confidence

 

[arunma]

Colin, you're right to suspect that vector analysis is extremely important in physics. What I would do is forget about it for now, and spend a few weeks studying it. Since you've already taken multivariable calculus, the hard stuff like double and triple integrals should be no problem for you. I would spend some time focusing on dot and cross products, line integrals, surface integrals (for which you should know how to parametrize a surface), and the vector derivatives such as the gradient, divergence, and curl. Study this, and you should be just fine.

The good news is that vector analysis isn't particularly difficult. I learned much of what I know about vector analysis during my freshman year, when I used to sit in the back of my integral calculus recitation section and read ahead in the book (it got me an easy A in vector calculus the next semester!). And I'm no genius, so I think that you should find the subject to be very straightforward. Just make sure you pick it up soon, because vector calculus is very important in classical mechanics and electrodynamics.

 

[AngeloG]

I'm in the same predicament. I was thinking of taking courses over again to re-learn, or just accept my grade and teach myself. However, I hear it's bad to retake courses. It looks bad on the transcript? Can anyone confirm this?

 

[colin.mcenroe]

Ok, thanks for the encouragement from everyone. I do know how to deal with double/triple integrals as well as dealing with polar/cylindrical/spherical coordinate systems, and I have seen the material (Stokes and Green's Theorems and all the relevant ones; the class I sat in on was very thorough), just not studied it. I also know how to compute line integrals as well as all of the dot/cross product stuff (I am currently taking advanced linear algebra as a supplement to my physics material I have coming up).

Any recommendations on a thorough but concise text on the material? I do have Div, Grad Curl and All That, but I am not sure if it is sufficient though I suspect it is.

As far as quantum mechanics, I will be taking my final lower division physics course that covers modern physics next quarter, so I will be exposed to that as well before I have to really dive into it. My dad also gave me his copy of Eisberg and Resnick on QM, so I will be sure to look through that!

Thanks for the advice everyone.

Also, proton, something reminds me that you went to the same community college as I did if I recall correctly (CSM, Skyline, Canada system). It is surprising that in one semester there is not enough time to cover the material required by UC to have the courses communicate properly!

 

[kdinser]

You have all the time in the world to learn what you need to know, the material is very straight forward and even makes sense to me and I tend to be pretty dense when it comes to math stuff. Go through Stewarts 4th or 5th editions chapters 12 - 16 and you should be set. Just blaze through what you already know and you should be ready for the fall.

Also, don't worry to much about what you didn't learn in your math classes, the important stuff will keep popping up over and over again, you will either master it when it comes along, or fall by the way side, either way, it will be your work ethic and ability that will decide.

Go to your professors office hours early on if you are having trouble, they will be able to judge if you are lacking some key knowledge that is needed to be successful in that class. Don't underestimate how useful your professor can be one on one; I've had some horrible lecturers who turned out to be fantastic when you were able to point out specifically what you didn't understand.

Good luck!

 

[^_^physicist]

I was put into a similar position. I had no "formal" vector or multivarate training, and was, by the advice of my crazy advisor, told to just skip it. He was about right, at least for me. It turned out that by just grabing a calculus book that covered the material and a few sample problems from the book "Div, Grad, Curl, and All That," I was able to pick up all of what I needed to know in a weekend, and I am by no means a genius (I will admit I am quick on the uptake in math, though). The next week I was able to manuver around in my classical mechanics course without much trouble.

So my advice would come down to, try to just re-hash/self study the material for a weekend or so with a text that has a focus on physics, and you can pick up most of what you need. And if all else, you can always sit in on a couple lectures (at least at my univeristy you can do this), without any obligations, and learn the material.

 

[jtbell]

Many or most intermediate-level electricity & magnetism textbooks start by reviewing the vector calculus that the course needs: surface integrals, line integrals, div, grad, curl, Stokes's Theorem, divergence theorem.

 

[proton]

Also, proton, something reminds me that you went to the same community college as I did if I recall correctly (CSM, Skyline, Canada system). It is surprising that in one semester there is not enough time to cover the material required by UC to have the courses communicate properly!

I go to community college in southern california. I do recall a thread where two junior college students admitted going to the same school, so it must have been you and someone else.

 

[colin.mcenroe]

I go to community college in southern california. I do recall a thread where two junior college students admitted going to the same school, so it must have been you and someone else.

Oh, sorry about the confusion!

 

[kant]

Hello,

I am a physics major and just transferred to UC Davis from a community college. My multivariable calculus course did not for some reason include vector analysis even though it tranferred as such. In other words, the requirement is met, but I don't have the knowledge. I did audit a course last semester at my community college where the professor actually did teach this material, but I was so overloaded with other classes (19 units) that I did not have the time to study it (nor the motivation). Anyway, I am going to start my upper division courses in the fall quarter, so I have plenty of time to "relearn" the material and have it sink in. Is this something I should do now, or is it something I will pick up as I go?

Thanks for advice!

Well, i am like you. I transferred to ucla from my local community college. Take it from me. you don t need to study vector analysis. Most people in my upper division math, physics classes forgot it anyway. It is just the nature of the matter. You might find it more productive to learn new stuff as you go.

 

[marcusl]

Ok, thanks for the encouragement from everyone. I do know how to deal with double/triple integrals as well as dealing with polar/cylindrical/spherical coordinate systems, and I have seen the material (Stokes and Green's Theorems and all the relevant ones; the class I sat in on was very thorough), just not studied it. I also know how to compute line integrals as well as all of the dot/cross product stuff (I am currently taking advanced linear algebra as a supplement to my physics material I have coming up).

Oh, I thought you said you never had vector calculus! Sounds like you're in pretty good shape already

 

[proton]

Well, i am like you. I transferred to ucla from my local community college. Take it from me. you don t need to study vector analysis. Most people in my upper division math, physics classes forgot it anyway. It is just the nature of the matter. You might find it more productive to learn new stuff as you go.

really? I was all worried about the possibility that I will transfer to UCLA and be behind everyone else! I'm certainly relieved now

 

[colin.mcenroe]

Yeah, I think it depends on your community college. I definitely don't feel behind everyone else here at UCD. The big difference for me is feeling somewhat average when in the past I definitely was near the top, but that is the nature of a university. It isn't that I am behind, it is more a feeling that there are students who are always going to be ahead. I am sure some of these people are able to do so without studying.

For now, I am taking math courses, which I am perfectly aware is not what I am best at. I can do the math, but the abstraction is not something I particularly enjoy. I will see how my physics courses go and whether or not I am feeling ahead/average/behind once I start them.