Which Jr. level physics course to pick?

[Angelo Marney]

Hi all,

I am a student in Mathematics who has recently discovered a small interest in Physics. I will be graduating next semester, but I will have the opportunity to take an extra class of my choosing. I have already completed the year-long Physics I and Physics II sequence covering elementary Classical Mechanics & Electromagnetism that most engineers take. I would like to ask what class would be the most interesting or useful to a soon-to-be Math graduate student. If it matters, I will likely be doing computational math or numerical analysis in graduate school, but I greatly enjoy pure math. I also like earth-science and chemistry a decent amount.

Mechanics - This course is an undergraduate course in classical mechanics at the level of the textbook by Fowles and Cassidy. The course includes particle dynamics in one, two, and three dimensions; oscillatory systems including normal modes; conservation laws; dynamics of a system of particles; motion of rigid bodies; central force problems; Lagrangian and Hamiltonian Mechanics.

Electromagnetism - This course is an undergraduate course in electromagnetism at the level of the textbook by Griffith. The course includes electrostatics; Laplace's equation; the theory of dielectrics; magnetostatic fields; electromagnetic induction; magnetic fields of currents; Maxwell's equations.

Thermodynamics - Concept of temperature, equations of state; the first and the second law of thermodynamics; entropy; change of phase; the thermodynamics functions.

Modern Physics - Foundations of the atomic theory of matter; kinetic theory; elementary particles; radiations; atomic model; atomic structure; atomic spectra and energy levels; quantum theory of radiation; x-rays; special theory of relativity.

At the moment, I am leaning towards electromagnetism, as I found it to be more interesting than mechanics. I am not too sure. Any suggestions are appreciated.

 

[mpresic]

These areas all are going to involve or not involve math depending on how they are taught. This is what I mean. Modern physics lists kinetic theory. Therefore you may think this involves probability theory, or elementary particles, that is going to involve algebraic structures. However, at the level that these are taught for a one-semester course, the professor may not involve you in the full treatment.

Mechanics will involve normal modes, This means linear algebra, Eigen(values) and (vectors) are going to play a big role, along with differential equations. If they present Lagrange and Hamiltonian mechanics, this involves the calculus of variations. Motion of rigid bodies, will involve Euler angles, quaternions. The solution to spin rates for a free anaxisymmetric bodies involve Jacobi elliptic functions,(special functions) but your professor will never get this far in.

Electromagnetics will involve you in potential theory, (which I find to be very dry). You will definitely see special functions and partial differential equations here.

The telling point is the textbooks. Does Fowles and Cassidy treat normal modes using linear algebra? or treat rigid body motion with quaternions or euler angles (I do not know). Griffith does present some rudimentary potential theory. Thermodynamics seems to be least math related.

Personally, I think I would go with Mechanics.

 

[Angelo Marney]

Thanks for the reply mpresic.

I was looking through Fowles and Cassidy and the very last chapter of the book (dynamics of oscillating systems) does in fact involve linear algebra (the eigenvalue problem). I greatly enjoy linear algebra and would love to see how the eigenvalue problem shows up in areas of physics. I know that it is very important in Quantum Mechanics, but I do not have the necessary prereqs to take Quantum Mechanics (I need Modern Physics), which kind of sucks. What worries me is that, as this is a one semester undergraduate course, we will most likely not get to the end of the book and/or I might only be exposed to the bear minimum of the most interesting topics (Lagrangian and Hamiltonian mechanics and eigenvalue problem associated with oscillating systems). I might try asking professors to see if it is possible to get Modern Physics waved for Quantum Mechanics, but this is very unlikely (and would probably add a very very significant amount of work to my semester). Even if I do not sign up for QM, it might be possible for me to at the very least, sit in on the lectures or watch the recorded videos. Its possible that this is a terrible idea because I will have absolutely no idea what is going on though.

Anyone have any thoughts on this?

 

[mpresic]

In the past, I have usually found professors receptive to waiving requirements on an individual basis. An undergraduate QM course at the level of Griffith, which after all is the textbook adopted in the proposed electrodynamics course, does not have exceedingly strong prerequisites, and I would think a mathematics about to be graduate would be considered acceptable. If you were a first semester Junior who felt like they did not want to be bothered with modern physics and rush on into QM, (this would eventually short-change the student from the full rigor of the physics program) it would be another story. But you are proposing to take one semester as a supplement to your mathematics program. Even the first semester of QM would touch on probability principles, Fourier transforms and analysis, and partial differential equations. For Hilbert spaces and topology, you would probably need a graduate course, which you can get in graduate school if you want it.

I do not think a about to graduate mathematician would find the one semester QM course is necessarily much harder than a one semester modern physics course, but only the professor can make that determination. Good Luck.

 

[ZapperZ]

Hi all,

I am a student in Mathematics who has recently discovered a small interest in Physics. I will be graduating next semester, but I will have the opportunity to take an extra class of my choosing. I have already completed the year-long Physics I and Physics II sequence covering elementary Classical Mechanics & Electromagnetism that most engineers take. I would like to ask what class would be the most interesting or useful to a soon-to-be Math graduate student. If it matters, I will likely be doing computational math or numerical analysis in graduate school, but I greatly enjoy pure math. I also like earth-science and chemistry a decent amount.

Mechanics - This course is an undergraduate course in classical mechanics at the level of the textbook by Fowles and Cassidy. The course includes particle dynamics in one, two, and three dimensions; oscillatory systems including normal modes; conservation laws; dynamics of a system of particles; motion of rigid bodies; central force problems; Lagrangian and Hamiltonian Mechanics.

Electromagnetism - This course is an undergraduate course in electromagnetism at the level of the textbook by Griffith. The course includes electrostatics; Laplace's equation; the theory of dielectrics; magnetostatic fields; electromagnetic induction; magnetic fields of currents; Maxwell's equations.

Thermodynamics - Concept of temperature, equations of state; the first and the second law of thermodynamics; entropy; change of phase; the thermodynamics functions.

Modern Physics - Foundations of the atomic theory of matter; kinetic theory; elementary particles; radiations; atomic model; atomic structure; atomic spectra and energy levels; quantum theory of radiation; x-rays; special theory of relativity.

At the moment, I am leaning towards electromagnetism, as I found it to be more interesting than mechanics. I am not too sure. Any suggestions are appreciated.

The frequent and most obvious question I will ask anyone asking this type of question on PF is this: Have you asked this question and talked to your academic advisor?

If you have, what was his/her recommendation? If you haven't, why not? This is the person who should have a lot more information about YOU than any of us. Presumably, the two of you could talk about this and come up with a suitable plan that should be beneficial to you.

Zz.

 

[sregmi]

Definitely Electrodynamics. Its really interesting development to the real electrodynamics, you may as well call it baby electro. You also get to see how all your math gets used plus i bet you will enjoy that class while solving laplace n Poisson's eqn in 3D. u will enjoy the class because you have a good math base and u can definitely learn physics if you don't have to worry abt math. I learned it the hard way since i only had ODE with little bit of linear algebra mixed in it before i took that class n believe me learning special functions wasn't funny at all in the beginning.
But learning Lagrangian and Hamiltonian in Classical mechanics is fun too but i hated the motion of rigid bodies.
I don't know why there is a pre-req for Q1 which is also an intro class n prolly use Griffiths Q1. But if u can get into Q1 class definitely take that one above all.