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1. Shooting method vs. finite differences for BVP

I am considering a second order ODE of the form y''(x) + f(x) y(x) = 0, with boundary conditions that y(x) = 0 at plus/minus infinity. Note that f(x) is complex for my case. It seems that the standard techniques for numerically solving this problem are (a.) the finite difference method and...
2. Ionizing solutions to the hydrogen atom

Are there any ionizing solutions for the hydrogen atom problem, where the electron breaks away from the proton?
3. Contradictory FBD's for simple pulley problem

I have a basic pulley problem which has been troubling me. Consider the system as shown in the attached picture. We have a massless pulley attached to the ceiling and a mass suspended from one side of the pulley. If we take the free-body-diagram by 'cutting' where the red box is, we find...
4. Generic coordinate systems

Say we have a vector field defined in R^3. That is, at every point p in R^3, we have the corresponding set (p, v(p)). In representing this field, as far as I can tell, we have a certain list of very general requirements. That seems to be a.) an origin, b.) three everywhere non-coplanar curves...
5. Example of a differentiable structure on R

Consider the manifold of the real-line R with a differentiable structure generated by the map x^3 : M \rightarrow \mathbb{R} . This example is given in a textbook I'm looking at, but I don't really understand how this can work. The inverse map is clearly not smooth at x=0. Do they mean that...
6. Compact sets in Hausdorff space are closed

First of all I just want to rant why is the Latex preview feature such a complete failure in Firefox? Actually it is really bad and buggy in IE too.... So I am reading into Foundations of geometry by Abraham and Marsden and there is a basic topology proof that's giving me some trouble. They...
7. Multiplication of fourier series

Say you have two functions, F(x,y), and G(x,y), and you want to expand them in finite fourier series. Let their coefficients be designated as F_ij and G_ij. When you multiply the two functions, you get X=FG, and this should also have its own fourier series, call its components X_mn. What is the...
8. Ionization by magnetization

I'm interested in the question of what strength magnetic field you need to fully or partially ionize a neutral atom. I'm fairly sure this is possible but I'm not very familiar with quantum physics, atomic physics, solid state physics, and so on. I'm familiar with the "classical analog"...
9. Understanding in abstract algebra

In algebra, do you just base your understanding off the pure definitions and groups? I am learning some multilinear algebra, seeing a lot of talk about rings, algebras, modules, etc. and I can't help but thinking it's all just frivolous, pointless definitions. That's partly because I just can...
10. No difference between covectors and functions?

I'm reading into an introductory book on manifolds (Tu) and they start out by showing vectors are isomorphic to derivations at a point. They go on to introduce covectors, k-tensors, and then I've just gotten to the point where they introduce the "d" operator which constructs a 1-form from a...
11. Diffusion interpetation

Something has been bothering me recently regarding a diffusion problem. Consider a source of particles in a box, diffusing outwards. Set the boundary conditions so that the density is zero at the edge of the box. We can solve this problem in "steady state" and we find essentially a parabolic...
12. Practical questions on wireless internet bandwitdth

(1) Sometimes I notice that the bandwidth goes up a lot after I start getting a large feed. Like, my internet might be going pretty slowly, then I start downloading a large file and my internet connection moves up to 24 or 36 Mbps, loading web pages very fast, despite the fact that I am also...
13. What is the purpose of PDE research/study

I have flipped through the first few pages of Evan's PDE book lately, and I am considering taking a graduate PDE course in the fall. However I don't really understand the purpose of PDE research. Not that I really understand the purpose of ODE research or even analysis research for that matter...
14. DG vs. PDE course

I am trying to decide between two different graduate math classes in the fall. These are the only classes that sound really interesting to me, as well as fitting in with the rest of my schedule. My other courses will consist of several physics type courses, notably, Jackson's electrodynamics...
15. Choice between two grad math classes, DG vs. PDE

I am trying to decide between two different graduate math classes in the fall. These are the only classes that sound really interesting to me, as well as fitting in with the rest of my schedule. My other courses will consist of several physics type courses, notably, Jackson's electrodynamics...
16. Particle collisions collapse wave function?

I am imagining the collision between two subatomic particles. For the particles to have collided, do we say that the spatial wave functions for each particle must have collapsed to the same point? Or do we say that the particles are just in a very close vicinity, and the wave functions need not...
17. Preparing for Jackson Electrodynamics

I would like to know recommendations for the best way to prepare for Jackson's electrodynamics next Fall. I have taken Griffith's E&M as well as the usual undergraduate math (linear algebra, advanced calculus, complex variables, probability). I realize there have been some similar posts to this...

My best offer for graduate school has turned out to be University of Wisconsin - Madison for the Department of Nuclear Engineering and Engineering Physics. I plan on focusing on theoretical/computational plasma physics and magnetic confinement fusion. Does anybody have any personal...
19. Rigorous statistical thermodynamics?

I took classical (engineering) thermodynamics a few years ago, and this semester I am taking a statistical thermodynamics class from the physics department. We are using the book "Fundamentals of statistical and thermal physics" by Reif, which seems to be a pretty good book. Unfortunately I...
20. Intro to Diff. Geom. PLEASE COMMENT.

I am taking an introductory course in differential geometry this semester and I want to try and sketch my knowledge so far. We are using the book "Elementary topics in differential geometry" by Thorpe, which from what I have read, provides a fairly unusual treatment. I am looking for...

This is my all-world squad for 2009, in 4-4-2 formation: Van der Sar Evra - Vidic - Chiellini - Clichy Messi - Fabregas - Xavi (Hernandez) - Ronaldo Kaka - Ibrahimovic Think you have a better squad? Let's see it...
22. Schools Meeting with graduate school director, what should I do?

I am applying to graduate schools for next fall and one of the chairman of one of the programs is visiting my campus on next friday for academic reasons. He directs the program at a school across the country, so this turns out to be a very good chance to meet him. I have worked out an...
23. Conceptual Real Analysis

I have been taking real analysis II this semester and I am starting to get a better grasp over the broad subject of analysis and integration. However, I feel like my understanding is completely problem-oriented. I tried talking to a colleague of mine about real analysis in a conceptual...
24. Preparing for GRE MATH Subject test

I will be taking the GRE Math subject test this next Fall and I need to start preparing for it this summer... I have been looking around on the internet and it seems like there's very few practice tests available. Has anyone else prepared for this test and can give me some advice on how to...
25. Why is volume rated at 0 decibels?

I got a Denon stereo receiver in this past year and I noticed that the volume meter starts at something like -70 decibels and moves up through 0 decibels. I've also noticed on other audio equipment that the 0 decibel rating is linked to some kind of amplifier power level or something. Why is the...