I think It has something to do with the fact the the indefinite integral of 1/t is defined from 1 to x (because there is an asymptote at x=0), but if you are considering e raised to the power of that integral, I don't think there is a need to take into account the original complication. I'm...
I always used ρ for spherical coordinates and r for the xy-plane. But as long as your equations are consistent with what you are trying to do, it doesn't matter if you draw a little duckie as a variable.
Try to think of the reason why the absolute value bars are there in the first place. And then try to reason out why they would be dropped when the natural logarithm is eliminated.
Yep, looks good. If you want to check yourself, you can always draw it out in both coordinate systems (they should be close to the same place if the graphs are drawn hastily).
That was a very helpful breakdown; thank you, snowstorm. I think I now have a solid idea of what is expected of me and where I should set my goals. It is an appreciably long list of criterion, but I suppose that it can be a good thing if I aim to be more prepared than the average applicant...
I didn't mean to completely shoot down UH. It's been growing rapidly in the past few years and all of that, and the opportunity for undergraduate research is abundant. It just seemed like next to my high school classmates going to Caltech, MIT, Rice, etc. I felt like I was a little worse off...
I haven't even begun thinking about what I want to do after graduate school. I just know that I greatly enjoy learning about the universe; physics and math are just what seem to be the best medium for accomplishing that. But as you intimated, I might have the idealized notion of eventually...
MIT Opencourseware 8.01. Google it. It has video lectures by the wonderful prof. Lewin, including accompanying practice exams and solutions. Ocw is a life saver for some of the "gateway" undergraduate math and physics courses.
I am currently a freshman at the University of Houston as a Physics and Mathematics double major. From what I understand, UH isn't the most reputable university; however, I am dead set on doing whatever it takes to get into a top graduate school for anything Math or Physics related.
My...