# Freshmen Mechanics

## Main Question or Discussion Point

Since I'm attending a community college (thankfully this is my last semester before I transfer), I got a very poor education in my introductory mechanics with calculus class. Also, I wasn't motivated at the time so I didn't self- study much.
My question is what would be better preparation for my upper-div courses: the mechanics or the math?
How much of the mechanics will be useful for upper-div physics courses? I know some material like rotational mechanics, energy, etc are important, but what about sound and fluid dynamics, etc? Since the intro mechanics class is designed for prospective scientists and engineers, I assume that a lot of the material is useful for engineers but not physics majors.
Also, I've heard that the upper-div will focus alot more on math. So would it be better if I reviewed all of the mechanics, or to self-study as many math methods from Boas? Subjects like calculus of variations, tensors, PDEs, etc.

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## Answers and Replies

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FredGarvin
How do you know that you got a poor education because of it being a community college? What do you have to compare that against? Probably during the first two years you're going to chew a lot of the same dirt as engineering majors.

The main thing from mechanics that you need are free body diagram knowledge and basic trig, really thats all I kept see coming up in upper division physic courses and double integrals

At the lower division level, it's really hard to say that either physics courses or math courses are more important than the other. You need to take both in order to do well in the upper division math classes. The math courses that you need to take in order to take upper division physics are calculus 1 and 2, multivariable calculus, differential equations, and linear algebra (the last two are usually combined into one course). Any math beyond this is superfluous, and probably not terribly useful for upper division physics.

BTW don't worry about calculus of variations, tensors, or PDEs for now. PDEs are used in upper division quantum mechanics, and tensors are used in both special and general relativity. But you learn this material on the fly (in fact I think it's easier to learn PDEs in the context of physics). So there's no need to take classes on these subjects. But hey, any self-study you want to do is always useful.

"How do you know that you got a poor education because of it being a community college? What do you have to compare that against? Probably during the first two years you're going to chew a lot of the same dirt as engineering majors."
I'm comparing that to how much I got out of my modern physics class. I put a lot more effort into the modern physics than mechanics. I spent probably 3-4 hours a week studying for the mechanics compared to about 6-8 hours for the modern physics

"The main thing from mechanics that you need are free body diagram knowledge and basic trig, really thats all I kept see coming up in upper division physic courses and double integrals"
That's it? If you're right, then I've been worrying way too much.

"Any math beyond this is superfluous, and probably not terribly useful for upper division physics."
"So there's no need to take classes on these subjects"
Well I've heard many people mention how much easier their upper-div physics classes were when they took math classes like PDEs, upper-div linear algebra, etc.

Another question I have: do most physics majors double major in math because its helpful for grad school primarily or also because its helpful for the upper-div physics?

Thanks for the advice guys.

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Another question I have: do most physics majors double major in math because its helpful for grad school primarily or also because its helpful for the upper-div physics?

Thanks for the advice guys.
Many people do because the requirements aren't that much more so they figure it couldn't hurt... or they have a real interest in the subject.

I personally find the elegance and beauty in mathematical theories to be equally as interesting as physics, so that is why I want to pursue a double-major. I also don't know if I will want to go to graduate school for pure mathematics or physics, so I figured i'd keep my options open.

I also don't really understand what I need to know at the upper-divison level, so I figured I would just take as much as I could. All maths make you smarter even if you don't apply them directly.

As you know Proton, I too, am in your position in regards to community college so I appreciate your concerns. This thread is a good thread for me to read through and get an idea as to what to expect, as well.

Thanks,
Trevor or otherwise colloquially known as cP

Another question I have: do most physics majors double major in math because its helpful for grad school primarily or also because its helpful for the upper-div physics?

Thanks for the advice guys.
I double majored in physics and math. To be honest, most of the applied math that I know, I learned in physics. Although grad schools do look favorably upon people who have second degrees in math, that wasn't my primary motivation. The reason I did a seocnd major in math is because I like math in its own right. Being able to incontrovertably prove things has a certain appeal. And getting into the formalism is very interesting, because you begin to understand why things work in mathematics. As a math professor of mine once said: when you write down a definite integral, you're writing down an entire sentence of information and condensing it into that symbol (for example, you're saying things about the integrand's continuity, the completeness of the interval/domain of integration, etc.). It's interesting to be able to know what exactly those mathematical symbols mean.

So I like math as a subject of its own, but aside from the basics of single- and multi-variable calculus, I never found it particularly helpful in learning physics.

OK I see, most double majors do it because they really enjoy math.

Back to the original topic, is all you really needed to know from freshman mechanics basic trig and free-body diagrams?

Being both a tutor and workshop leader for lower-division physics classes, and from talking to the professor I work under concerning this very same topic, I can safely say-

Lower Division Physics courses are designed for developing a method of "looking" at problems. Of course the two primary skills required to "look" at a problem, is trig and the ablity to draw free-body diagrams; at least for mechanics' sake.

So back to your orignal question concerning what you should look at before you start an upper division mechanics course... I would say the math is going to be the stickler. If you paid attention at all during your lower division physics class, I would be their had been a good chance that you understand how to approach the topic, at least from a " just lookin' " point of view.

Of course the safe bet to do is to email the professor that teaches the course before you take it and see what they think. Maybe try to get ahold of the textbook early and look through what math is expected of the students during the derivations (often times, it is very simple systems of differential equations, sometimes not, but for the most part they aren't normally that bad).

Ok thanks for the great advice. I definitely know my trig and free-body diagrams. I was just concerned that I had to remember all the derivations angular momentum, torque, etc with the cross products, etc. My professor never went over the vectors and barely went over the calculus.