Should I Take Mechanics Without the Advisory Pre-Reqs?

[NathanExplosion]

Hi everyone, I have a question that I'd like to get some of your opinions' on. I'm currently making up my schedule for next semester, and I'd like to take an upper-division class aptly named "Mechanics" The course doesn't have a website, so I don't have a syllabus handy, but what concerns me are the pre-reqs. They list Modern Physics as an advisory pre-req, so it's not enforced. They also claim a course on ODEs is a pre-req, although apparently it's not enforced either (I was able to register for the course and I don't have either Modern Physics or a course on ODEs done yet).

There is a guide on my school's physics dept's website saying: "Note: strong students can ask the instructor of 'Mechanics' about taking it in the Sophomore year in spite of its Modern Physics and ODEs prerequisites." The course description says:

"An in-depth study of classical mechanics, from the Newtonian to the Lagrangian and Hamiltonian formulations. First, Newtonian mechanics is reviewed and applied to more advanced problems than those considered in Physics I or Honors Physics I. The Lagrangian and Hamiltonian methods are then derived from the Newtonian treatment and applied to various problems."

With that said, does it sound like these topics would require rigorous preparation in ODEs, in your opinions? The only (somewhat relevant) math/physics courses I've taken are Physics I/II, Calculus I/II, and Linear Algebra. I'll be taking vector calculus next semester (theoretically alongside Mechanics).

Sorry for being verbose, guys, just want to make my decision now whether or not to take the course. That way, if I decide to drop it, I can sign up for Modern Physics before it fills up!

Thanks to everyone!

 

[Bitter]

When I took my mechanics course, I need series solutions to differential equations, Fourier series and transforms, vector calculus, matrix algebra, complex functions, and partial differential equations to do well in it. I find it hard to do well without any of that.

 

[NathanExplosion]

Thanks for the response! That's a lot more math background than I have, in which case I think it'd be best to put Mechanics off for a bit!

 

[^_^physicist]

Let it be stated that I managed to get a fairly strong B and B+ in a mechanics like the one you posted below as sophomore with only a course on ODE's (no other formal mathematics background). So I wouldn't say that it is impossible. It just takes a time commitment to wrap your head around the methods.

I think it would be best that you talked to others in the department, maybe look up the professor that teaches it and see if you can get ahold of the syallabus earily so you can find the text and take a look at it.

 

[arunma]

To be honest, I'd be a bit more concerned about the fact that you haven't taken vector calculus. When I took analytical mechanics (that's what it was called at my undergraduate school), the various techniques of multivariable integration were pretty important, especially in the section on gravity. You might want to think about differing mechanics until you've taken vector calculus.

As for the ODE issue, personally I think that if you just keep a textbook on differential equations handy, you should be good. Differential equations are extremely important for physicists, but to be honest, I learned most of the diff eq I know from my physics classes rather than my math classes.

 

[Coto]

I completely disagree with what Bitter wrote.. and since you never mentioned if or if not you have done vector calculus and linear algebra, then I'm going to assume you have at least this level of mathematics. It seems weird that you would have access to (part of) the course without intro calculus and linear algebra.

Anyways, I had essentially the same course about mechanics.. went through your course description, formulating the lagrangian and hamiltonians as well as techniques in manipulation based off of classical mechanics problems.

1) ODE's are needed to the extent that you know how to solve a basic linear differential equation.. i.e. introductory calculus. You don't need knowledge of transforms or series solutions for well formulated mechanics problems, and as an introduction to lagrangian and hamiltonian, its pointless to give difficult examples that no longer re-enforce the concepts at work, but rather the method of solving a differential equation. In fact, we never had to solve any ODE's.. the most you would have to know is multidimensional calculus (i.e partial derivatives and vector calculus). Very rarely, if it all, was it required to solve for the equations of motion of a system (x(t)).

2) You definitely don't need PDE's and complex functions.. a course on PDE's would help understanding some concepts, but is definitely not needed to do this course. Fourier transforms are not used at all either.

Chances are this is an introductory course on advanced analytic mechanics.. and it's more about the concepts then it is about utilizing the full power of the concepts.

 

[NathanExplosion]

Actually Coto, I mentioned I've taken Calc I/II (includes that little bit about diffeq's at the end) and Linear Algebra.

 

[jtbell]

I think it would be best that you talked to others in the department, maybe look up the professor that teaches it and see if you can get ahold of the syallabus earily so you can find the text and take a look at it.

Definitely talk to the instructor if you have any doubts. He can tell you whether a prerequisite is significant in terms of the material that he actually covers in the course. Sometimes prerequisites are used to discourage weaker students from taking a course, or to make sure that students have a certain general level of sophistication and not because the specific content is actually used extensively in the course. It's also dangerous to compare what looks like the same course at different universities. Courses with different prerequisites may actually be taught at different levels of sophistication, even if they use the same or similar textbooks.

 

[Bitter]

I completely disagree with what Bitter wrote.

I'm not sure why you disagree with what I wrote. I told you what I needed. I din't say everyone else needs it. My course was callled intermediate mechanics, but as far as I know, there is no introduction mechanics at my school.

 

[math_owen]

Nathan,

The course uses the book "Analytical Mechanics" by Fowles n Cassiday. I have it sitting next to me. I have not taken the course, but I know many who have. You can probably look at it online at amazon and see if you can hack it. It might be tough without calc 3 and diff-eq under your belt.

Here you go, the link to amazon. It appears you can look inside.
https://www.amazon.com/dp/0534408133/?tag=pfamazon01-20

 

[math_owen]

Nathan,

As far as Modern physics, its considered one of easiest physics class at the school. If you're a physics major, you absolutely must take that class w/ the lab. Get it out of the way would be my opinion before the rest, even if you take mechanics with it. Modern is a prerequisite to Thermo too there.

You can sign up for EM, Waves/ Optics and Mechanics w/o Modern. As far as I know, Waves and Modern are interchangeable for your sophomore year.

The book for Modern is "Modern Physics" by Serway, Moses, Moyer.

Let me add, a co-req to EM is applied real analysis 341, it should be called calculus 5 intro to PDE's, but whatever. That's an easy math class, but I'm told it's used extensively with the EM classes. The 2 EM classes use the book by Griffiths.

 

[math_owen]

Sorry to post so much. Maybe you're not aware of the uber-kids at our school. Some kids come into their freshman year and skip calc 1-3 or 1-4. Those are probably the kids they have in mind. Usually the same ones that take the honors classes.

 

[NathanExplosion]

Thanks for all the info, math_owen; it's invaluable to get an opinion from someone who knows a good deal about the exact courses one is talking about! I'll probably take Modern w/ lab and Waves/Optics this semester.

 

[math_owen]

No problem dude. That's what the forum is for. Maybe someday we'll have a representation of all schools - ok, maybe not.

That's a common path you said. The spring is followed up with Thermo and the Electronics lab.

You'll cover calc 3 next semester, and diff-eq in the spring.

The only other advice I could say is to take more math. If I've heard one complaint, it's that learning math from the physicists sucks - that's from the physics students.

Half my math classes are physics majors, even crazy advanced ones.

I suggest if it fits you take MAT 200 Proof this Fall. Then you're able to take things like analysis, topology, and differential geometry.

If you took 200, then in the Spring you could take 319 analysis. The difference between 319 and 320 is about 2 to 3 chapters of the book. 320 is for math majors, or those who know for certain they're going theory. 319 is for teach-preps and other sciences. Personally, I say go 320, but I'm math.

As is, the following fall you'll take MAT 341 Applied Real with your EM class. Then in the spring you'll take MAT 342 Applied Complex. That's pretty typical. As a math guy I thought those classes were easy. But I had MAT 320 Analysis under my belt. So epsilon-delta proofs were already in my tool box.

That's if you're going theory. If you're going applied physics. Then I would suggest you take a lot more EE and Materials Engineering classes.

There's a kid who graduated this spring with a double in Physics and Materials Eng. He's off to Harvard's physics this fall.

You're at a great school Nathan, work hard, and it'll pay off. Our school is nick-named an "ivy league feeder". Often our students in math and physics, if they did really good, go to the top 5 schools.

 

[NathanExplosion]

No problem dude. That's what the forum is for. Maybe someday we'll have a representation of all schools - ok, maybe not.

That's a common path you said. The spring is followed up with Thermo and the Electronics lab.

You'll cover calc 3 next semester, and diff-eq in the spring.

The only other advice I could say is to take more math. If I've heard one complaint, it's that learning math from the physicists sucks - that's from the physics students.

Half my math classes are physics majors, even crazy advanced ones.

I suggest if it fits you take MAT 200 Proof this Fall. Then you're able to take things like analysis, topology, and differential geometry.

If you took 200, then in the Spring you could take 319 analysis. The difference between 319 and 320 is about 2 to 3 chapters of the book. 320 is for math majors, or those who know for certain they're going theory. 319 is for teach-preps and other sciences. Personally, I say go 320, but I'm math.

As is, the following fall you'll take MAT 341 Applied Real with your EM class. Then in the spring you'll take MAT 342 Applied Complex. That's pretty typical. As a math guy I thought those classes were easy. But I had MAT 320 Analysis under my belt. So epsilon-delta proofs were already in my tool box.

That's if you're going theory. If you're going applied physics. Then I would suggest you take a lot more EE and Materials Engineering classes.

There's a kid who graduated this spring with a double in Physics and Materials Eng. He's off to Harvard's physics this fall.

You're at a great school Nathan, work hard, and it'll pay off. Our school is nick-named an "ivy league feeder". Often our students in math and physics, if they did really good, go to the top 5 schools.

I never heard the ivy-league feeder thing before, but it seems apt. There are some great minds at SB for math and physics students (although we may not win any awards for our liberal arts/humanities departments )