What math should i review before taking a course in mechanics

[jasc15]

I am registering for a mechanics course for the fall semester, and would like to know what math to review to prepare myself.

The course description is as folows:

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 PHY 131 or 141. The Lagrangian and
Hamiltonian methods are then derived from the
Newtonian treatment and applied to various problems.

Thanks

 

[mgb_phys]

Make sure you are comfortable with calculus and matrices before you jump into hamiltonians.

 

[Pseudo Statistic]

Is the calculus of variations covered within the course?

 

[^_^physicist]

From what it looks like, I would suggest reviewing Diff. Eqs. I know many mechanics courses also suggest Linear Algebra, but I didn't have it when I took mechanics and any linear algebra given in the class was stuff I had picked up pretty quick.


If you are looking for a deeper understanding of mechanics, some calculus of variations work wouldn't hurt...but I don't think it is absolutly necessary to pass this course.

 

[Brad Barker]

Is the calculus of variations covered within the course?

in my experience, it is.

you might be asked to solve a few ODE's. in my course, i recall having to solve a nonhomogeneous second order equation once during a homework assignment.

if you end up covering inertia tensors, you'll be building matrices with elements given by multidimensional integrals.

so you'll probably be good with the calc sequence and an introductory course to diff eq's.

 

[CPL.Luke]

I too am taking a course in mechanics this fall, however I am curious what exactly is "the calculus of variations"?

 

[tacosareveryyum]

Calculus of variations is a field of mathematics that deals with functionals, as opposed to ordinary calculus which deals with functions. Such functionals can for example be formed as integrals involving an unknown function and its derivatives. The interest is in extremal functions: those making the functional attain a maximum or minimum value.

At my university we have 2 mechanics classes. An intermediate mechanics where we deal with rigid systems, keplers laws, periodic motion, chaos. Then we have a second "Advanced Dynamics" course that introduces Lagrangian/hamiltonian dynamics, calculus of variations, coupled pendulums, ect.
During intermediate mechanics all I needed was some calculus (about calc 2 level) and differential equations. We solved a lot of differential equations. They were mostly homogeneous and second order.

 

[robphy]

Don't forget algebra, geometry, and multivariable calculus [especially the chain rule].

You might wish to familiarize yourself with various coordinate systems [which may be used to describe your configuration space].

In addition, you might wish to familiarize yourself with index notations (including summations and component notations).