Preparing for University: Advice & Tips

[Chewy0087]

Hey there again,

I'm looking for some advice on preparing for university, I've applied and luckily received offers, and the current work we're doing in school is very manageable so I intend to look further ahead,

so my question is, what can I do to prepare best for university?

Perhaps more specifically, having looked at a bit of Lagrangian/Hamiltonian mechanics (i understand it's extremely useful and an important topic), would that be understandable/a feasible thing to attempt to learn this year? I'm currently taking Physics, maths & further maths but I have no illusions that much of the later on mathematics or even intermediate/beginning mathematics will be unrecognisable.

Also would learning Lagrangian mechanics be terribly helpful or do you think there's any other topics i'd do well to spend extra time on before beginning? before you do ask I've looked at the syllabus of the universities in question and no-where can I see a specific mention to Lagrangian/Hamiltonian mechanics however there are mentions to "Classical Mechanics", with little extra information...

Thank you

 

[Phyisab****]

Its been a while since I took intro physics so take this with a grain of salt. But especially for exam taking the lagrange formulation could provide a very powerful way to quickly check your answers.

 

[ice109]

take the above advice with a huge grain of salt. no one ever checks there work on exams using lagrangian or hamiltonian formalisms.

learn lots of math. find which calculus book is used at the university you'll be attending and do every problem.

 

[Phyisab****]

Yea just learn calculus if you haven't beaten that to death. Don't try to get ahead of yourself it doesn't work.

 

[Chewy0087]

Hmmm, what parts of calculus should I focus on? Or everything?

Are there bits of calculus that i would be using more than others?

 

[Phyisab****]

You will need every bit of it at some point, you can't really get away with skipping anything. Like ice said, get a book and do every problem. If you do that you will be way ahead of most of your classmates. Not just in calculus knowledge but in mathematical maturity, discipline and studying skills.

 

[ice109]

everything. do it all.

if you just do every problem the learning will take care of itself.

 

[wisvuze]

Lagrangian/Hamiltonian mechanics before knowing calculus..? How much Lagrangian/Hamiltonian mechanics do you actually know

 

[Chewy0087]

Lagrangian/Hamiltonian mechanics before knowing calculus..? How much Lagrangian/Hamiltonian mechanics do you actually know

I know absolutely nothing in regard to Lagrangian/Hamiltonian mechanics I'm afraid

In terms of calculus we've covered the basics to quite a good degree;
Simple differentiation, implicit differentiation
Integration by; parts, substitution. Volume of revolution

we've also covered some simple differential equations (rate of decay etc)

could anyone recommend a really solid calculus for physics book with a wide range of difficulty?

 

[diazona]

That should be enough for you to work through the derivation of the Euler-Lagrange equation, and doing so would be good practice with the math. The main advantage of starting to learn Lagrangian and/or Hamiltonian mechanics (which is collectively called "classical mechanics" in course catalogs) now would be that you'd have more time to get used to them, and you may find it easier to follow a classical mechanics class when you do take it.

If you want to go on learning more math, I'd suggest focusing on linear algebra (the theory of linear operators, including matrices and vectors). That stuff gets used everywhere in physics. After that in order of importance, complex numbers and then differential equations.

 

[JD88]

You should probably learn multivariable calculus and vector calculus.