Maximizing Success in Physics: Strategies for Getting Ahead in Your Studies

[Opus_723]

First, some background. When I was a kid, I used to be way ahead of the class in every subject, to the point that the school wanted me to skip several grades. But a bunch of really traumatic family stuff happened that turned the last ten years of my life into a sinkhole, resulting in my grades falling through the floor, to the point that I barely got into a small, relatively unknown liberal arts school and then nearly flunked out my first year here. Since that first year though, I've entered the physics program, and have since had straight 4.0s every quarter. I'm finally approaching my old pace, but I'm terrified that's its too late to redeem myself. I hate to sound like I'm looking for sympathy, or, even worse, to sound pretentious. But I want my full meaning and desperation to come across.

I'm currently breezing through my physics courses with little effort. I'm learning a lot, but I feel that I could be doing considerably more. However, I feel like simply working ahead in the book won't do me a lot of good, since I have to go over all of the same material in class at some point regardless. My idea has been to concentrate on the material we have covered so far, becoming as fluent in the basic concepts as possible. I have been trying to find as much material online as possible from top schools, using resources such as MIT open courseware, to make sure I fill out any gaps in my school's physics curriculum. Also, I have found highly regarded textbooks such as Spivak's Calculus and the Berkeley Physics Series in my school library and intend to go through them in order to review previous material at a higher standard. Lately I have been doing all of the odd-numbered problems in my physics book, which is far more than assigned. My school also has a stash of freshman physics books very similar to ours but by different authors, and I thought I might check them out and specifically try only the problems rated most difficult. I'm also scraping together what little money I have to buy some basic equipment to perform simple demos in my house, just to keep things fun. One of my biggest fears right now is that I don't know how to gain any practical experience outside of the very basic labs that we do for class.

But I'm looking for more ideas. What is the best way to get ahead and/or develop a high command of the material? Are there any flaws in my current approach? Is it worth it to try and learn subjects ahead of time, even if we are going to cover them in class anyway? Or is it better to concentrate on becoming fluent in what we've already covered?

Edit: Forgot to mention that I'm a freshman in the program, just getting ready to start my first electricity and magnetism class. As far as math goes, I've taken vector calculus, but no linear algebra or differential equations yet. So that should give everyone an idea of what level I'm at right now.

 

[genericusrnme]

Maths, lots of maths, lots of linear algebra and group theory if you want to quantum mechanic
Introduction to Linear Algebra - G Strang
Linear Algebra - Hoffman
Obviously mathematical methods, I'd hold back a little on the spivak and analysis type books for now. It is good to know the rigor behind the calculus but for now you really don't need it. Try M Boas' Mathematical Methods, it covers most of the maths you'll need in undergrad courses.
There's plenty of other maths you'll need to learn but I'd have to give you a massive list of books since what you need to know is far less in depth than what is covered by a whole book, when you encounter some new maths you should be able to find where to look for it yourself.
Once you have some maths behind you I'd go for something that derives its equations from an action principle, if you're anything like me you'll find an action derivation much more satisfying and insightful than most of the 'just apply F=ma' type stuff you get early on.
Goldstein - Classical Mechanics (the first few chapters)
Landau and Lifgarbagez - Classical Mechanics (my favourite book on the basics of classical mechanics)
For E&M I'd start of with Griffiths' Introduction to Electrodynamics perhaps followed by some Jackson if you feel up to it.
For QM AVOID Griffiths' book at all costs. Go for something like
Landau and Lifgarbagez - Quanum Mechanics, non relatavistic
Sakuraii - Modern Quantum Mechanics
Shankar - Principles of Quantum Mechanics
That should be enough to get you a pretty good head start

edit;
Also, I wouldn't spend money on doing labs at home, everything that you can test at home is 1. boring as hell or 2. already tested to higher precision that you will be able to do at home.
You might want to avoid doing lots of drill problems, there's nothing wrong with them but as time passes you'll need to be able to learn about things without having a whole host of drill problems to do, you're better off making up your own systems and seeing how they behave and adventuring yourself.
As far as 'practical' experience goes... there's nothing you can really do that would be relavent to anything done today that you can do at a home lab.
You're better off sharpening your mathematical tools and understanding principles of physics, theoreical physics is always decades ahead of experimentation.
Unless you're into experimentation.. even then you're not really going to gain anything from a home lab.

 

[101physics]

This may sound like a daft opinion on how to get ahead, but I wouldn't focus so much on learning advanced material from bookwork until you get to that level in class or slogging through problem sets - sure its great to be interested and keep challenging yourself, but you don't want to burn out by pushing yourself too hard in your early years - there's a lot of work ahead . Instead, I would concentrate on trying to get some research experience (as much as possible) as these will stand out on your grad school apps when the time comes as well as forcing you to read current literature and learn how physics actually works. REUs are excellent programs (and I'm fairly convinced that by doing well in two REU programs is what got me accepted to grad schools). The problem is that REUs typically take juniors and seniors and so if you are really wanting to get experience now then I would get in touch with a prof at your school and try to get some work with him.That being said, I spent the summers of my freshman and sophmore years doing work and traveling that was completely unrelated to physics since I am hoping to spend the rest of my life in physics! Research experience either during the summer or with a prof is a much better plan than buying your own equipment and doing work at home.

Also, try to get involved in public outreach activities if there are any opportunities in your school as (I think) grad schools love this as it shows you are really interested in the work but also that you have experience of teaching and of explaining physics as well as making you really get your head around the material.

Take your time and enjoy the process as an undergrad - its in grad school that you really start to make a name for yourself and you'll be glad that you had fun as an undergrad while you're slogging away at grad school :)

 

[Angry Citizen]

It is imperative that you learn how to derive equations and principles. Do NOT memorize formulas. As an example, it is much easier to remember that the work-energy theorem can be derived by dotting both sides of F=ma with the velocity vector, recognizing that acceleration is itself a function of velocity, and integrating, rather than going through the trouble of memorizing it all - funnily enough, I can't even remember the final form at present, but that could be because I'm posting early in the morning. Sure, you could commit it to memory, but why bother?

 

[genericusrnme]

It is imperative that you learn how to derive equations and principles. Do NOT memorize formulas. As an example, it is much easier to remember that the work-energy theorem can be derived by dotting both sides of F=ma with the velocity vector, recognizing that acceleration is itself a function of velocity, and integrating, rather than going through the trouble of memorizing it all - funnily enough, I can't even remember the final form at present, but that could be because I'm posting early in the morning. Sure, you could commit it to memory, but why bother?

This is exactly what I'm getting at with my book suggestions

As far as what 101physics says, you do what to get plenty of research experience but I think that if you feel up to it you should be pushing ahead regardless. One small benefit of pushing ahead is that you'll be able to start reading current research and actually understand it that bit earlier.
I also feel that the baby physics you get when you're just told formulas without any hints towards their derivations like, the kinematics equations you are simply presented with before you have even touched on calculus, teach you nothing and at the best give you practice with basic algebra which imo you shouldn't have to spend more than a few days on let alone a year or so, or however long you have to keep using them for.
You should learn and derive directly from a set of principles or axioms.
Take F=ma as your foundation, solve the second order differential equations, see where they take you
Take stationary action as your foundation, solve the second order or coupled first order differnetial equations, see where you go.
In both of these cases you are learning about how things work.
If you take the sets of kinematic equations as your axioms then you learn the same about physics as you learn about how a car engine works from driving a car, imo.

The use of kinematics is just an example of course but equations being poofed into existence without any explanation happens a lot and, imo, is a terrible way to teach things, which is why I reccomended books which start off by stating a set of principles and derive things from there.


Although I am of the viewpoint that you want to learn physics for the sake of learning physics and bettering your understanding, if you're looking for job opportunities and the likes then you're probably better of focusing 100% on the content of your courses rather than pushing ahead.

 

[Opus_723]

Some great advice everyone, I really appreciate it. I may have chosen poor wording when I talked about buying equipment for home use. I chose the word demos specifically because I know I'm not doing anything particularly practical, it's mainly for fun, so I don't get too burnt out studying. But then I followed that up with my worries about gaining practical experience, and that was probably confusing.

I would definitely like to get beyond that algebraic equations we are learning now, although I think my courses have done a decent job of deriving them from calculus and really basic, separable differential equations. Differential equations is one of the subjects I am trying to teach myself now by working through MIT's online course, but if anyone has any suggestions for books, that would be great. I've only looked at one book so far, and it assumed a whole bunch of vocabulary and math that I've never come across. On the other hand, the MIT course seems a bit simple, and doesn't explain a lot of things.

Luckily, my school doesn't have a grad program for physics. They have purposefully decided to provide all of their research and teaching opportunities to undergrads, the only major requirement being that you've completed your freshman series. I should be able to teach a lab section starting in the fall of my sophomore year, and I should be able to get involved in some research around that same time.

And the book list is perfect. Exactly the kind of stuff I'm looking for. My school library doesn't have all of those, but we seem to have a good chunk.

 

[genericusrnme]

Boas's book covers the techniques of differential equations that are generally assumed in most undergrad physics books and most of the time when more advanced methods are required they are generally explained in the physics text. You'll be surprised at the amount of maths you'll pick up from physics textbooks.