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1. 3 math classes in one semester- too much?

I'm taking partial differential equations, modern algebra, and Fourier analysis this semester. It's definitely doable if you prioritize.
2. Physics REUs for 2011

I also got into PPPL NUF, but I haven't been matched with a site yet.
3. This might be serious

Don't even do that (elfboy's suggestion), just do lots of practice with computational stuff.
4. REUs for current sophomores (and other summer stuff)

I think between 5 and 10 is good. The recs shouldn't be too bad, likely very repetitive, so it wouldn't be too much more work than doing a single one. Last year, I only applied to 3 things and got lucky, I guess. I'm planning on around 5 apps this year. What subjects are you interested in?
5. REUs for current sophomores (and other summer stuff)

I'm also a rising junior. I was able to snag an REU last summer, as a rising sophomore, so I think you're chances should be fine. It's certainly a bit random, but cast a wide net. You could tutor over the summer, get your own hours, and you'd still be doing something related to physics/math...
6. UChicago or Columbia

So, I've got 5ish days to decide which of these institutions (UChicago, Columbia) to attend next year. At UChicago, I'd like to double major in Physics and Economics. At Columbia, I am accepted at the engineering school and I would major in Applied Physics and minor in Economics. The main...
7. Fnet=ma 2008 #15

Homework Statement A uniform round tabletop of diameter 4.0 m and mass 50.0 kg rests on massless, evenly spaced legs of length 1.0 m and spacing 3.0 m. A carpenter sits on the edge of the table. What is the maximum mass of the carpenter such that the table remains upright? Assume that the force...
8. Fnet=ma 2008 #14

Thanks, I get it now.
9. Fnet=ma 2008 #14

Homework Statement A spaceborne energy storage device consists of two equal masses connected by a tether and rotating about their center of mass. Additional energy is stored by reeling in the tether; no external forces are applied. Initially the device has kinetic energy E and rotates at...
10. Green's Theorem well, sort of.

I forgot a factor of 1/8 that should be in the second expression when I factored, thanks for the help!
11. Green's Theorem well, sort of.

I realized my mistake, I had been thinking that I needed to get positive 32/15, but it all depends on the direction of the curve, which in my case was clockwise, and is usually taken to be counterclockwise. Is that correct?
12. Green's Theorem well, sort of.

Yes, that's what I had, but I factored it just a little bit in the above expression.
13. Green's Theorem well, sort of.

Homework Statement Evaluate \displaystyle \int_C y^2dx + x^2dy for the path C: the boundary of the region lying between the graphs of \displaystyle y=x and \displaystyle y=\frac{x^2}{4}. Homework Equations The catch is that you can't use Green's Theorem. The Attempt at a Solution...
14. Polar Double Integral

Hmm, to check it, I plugged both expressions into my calculator and they're spitting out different numbers. The rectangular one gives me around 28.4 and the polar one gives me around 10.6.
15. Polar Double Integral

Wow, I'm sorry for that typo. That would change things. Would the correct limits for r be \frac{1}{cos(\theta)}\text{and}\frac{2}{cos(\theta)}?
16. Polar Double Integral

That is the rectangular integral given in the book. I think the region is a quadrilateral-like thing that is enclosed by x=1,2 and y=rt(3)x, x/rt(3). I found the limits for theta by setting tan(theta)=rt(3), 1/rt(3) because then the thetas produce the necessary lines.
17. Polar Double Integral

Homework Statement Given the integral: \int_1^2\int_{\frac{3}{\sqrt{x}}}^{\sqrt{3}x}{{(x^2+y^2)}^{\frac{3}{2}}}dy \; dx. Convert to polar and evaluate. Homework Equations r=\sqrt{(x^2+y^2)} The Attempt at a Solution Ok, I've gotten bounds on \theta, \frac{\pi}{6} \le \theta \le...
18. Maximize Volume of a Rectangular Box

Homework Statement Find the dimensions of the rectangular box of largest volume that can be inscribed in a sphere of radius 1. Homework Equations v=w*l*h, Set the partials equal to 0, then solve a system, etc. The Attempt at a Solution I'm really just unsure of the constraints that...
19. Line/plane thing

Homework Statement Given some plane, 3x+2y-z=6, and a point (2,3,6) Find a line in the plane passing through that point. Homework Equations The Attempt at a Solution I tried finding the vector perpendicular to the plane, <3,2,-1>, but I'm not sure what to do with it.
20. Polar Partials

Homework Statement Why are the following not contradictory? r=\sqrt{x^2+y^2} \frac{\partial r}{\partial x}=\frac{x}{\sqrt{x^2+y^2}}=\frac{x}{r}=cos{\theta} and r=\frac{x}{cos{\theta}} \frac{\partial r}{\partial x}=\frac{1}{cos{\theta}} Homework Equations The Attempt at a...
21. Delta-Epsilon Multivariable

So that is epsilon? How would we find the radius of the disk then?
22. Delta-Epsilon Multivariable

Homework Statement Let f(x,y)=2x+3y. Let \epsilon be any positive number. Show that there is a disk with center (1,1) such that whenever P is in that disk, |f(P)-5|< \epsilon. (Give \delta as a function of \epsilon.) Homework Equations None. The Attempt at a Solution Um, I tried...
23. Ratio Test for Series Proof

What do you mean by the Binomial Formula? I'm still kind of confused after taking several days away.
24. Rejected by fate? or something.

I am a 10th grader in high school and I applied to a prestigious prep school in New England this spring. They were accepting late applications and would then place students on a waiting list. The only way off was attrition, for which they expected at least a few spots to open. The said they...
25. Ratio Test for Series Proof

If L>1 then the sequence would be unbounded right? Because the next larger term is always of a greater magnitude than the previous. If L is less than 1, then the sequence is bounded, and the limit goes to 0?
26. Ratio Test for Series Proof

Do you mean greater than 1, or am I really missing something? And how would I start the induction? Just that for some N, |a_{2}|>r|a_{1}|?
27. Ratio Test for Series Proof

How would I start that proof by induction? How can I verify that |a_{2}|> r|a_{1}| . Also, for the second part, once I show that |a_{n}| tends to \infty isn't it basic logic that a_{n} cannot approach 0?
28. Ratio Test for Series Proof

Homework Statement Show that if Lim|\frac{a_{n+1}}{a_{n}}| = L > 1, then {a_{n}\rightarrow \infty as n\rightarrow\infty Also, from that, deduce that a_{n} does not approach 0 as n \rightarrow \infty . Homework Equations The book suggests showing some number r>1 such that for some...
29. SAT Subject Test in Physics

Oh, I found out how to do it, just use v^2=2ad and work it out. EDIT: Sorry for the obnoxious triple post.
30. SAT Subject Test in Physics

Wait, v doesn't equal a/d, I don't know what I'm thinking...