Recent content by df606

I see what you're saying. In other words, if you laid all the vectors head to tail, you would try to get a magnitude as close to zero as possible. I think I see a way to solve this recursively. Start with one vector in some arbitrary angle. Add another vector, starting at the tail of the...

I'm working on a programming project, and I've got this problem I don't really know how to describe or approach. Given a point and a number of lines extending from the point, I want to find the best angle (in 3d) to maximize the distances between the lines. The 2D equivalent would be to simply...

That explains things. Thanks!

I'm trying to read this book "Automata, Computability, and Complexity" by Elaine Rich and on page 75 it defines this function: \delta'(Q,c) = \cup\{eps(p):\exists q\in Q((q,c,p)\in\Delta)\} I've never seen the union operator used in this way. What does it mean? Apologies if this is in the...

Thank you Vanadium. I didn't know that about the GRE. I neglected to mention in the original post that I plan on switching to physics. Of course applying to grad school in physics without a degree in physics would be absurd. I've already gone over my school's physics program requirements and...

Thanks, it's good to know all is not lost. I've come so far in my CS program that I might just double major instead of switching entirely, and in that case, getting above a 3.0 would be easy... but I would be in school for a bit longer.

(I wrote a lot of text so scroll to the bottom if you want a synopsis) I'm a CS undergrad going to a crappy public school and recently I decided that I want to switch majors and get a PhD in math or physics. I've been interested in both subjects for a long time, math has been a big theme...

The answer is y=xy'\pm a\sqrt{(y')^2+1} I wish I could just differentiate twice cause that makes things so much easier but I can't. I used the equation you got as the slope for my line. That gives you a line that has the right slope but it doesn't intersect the circle at the right spot. The...

Homework Statement Find a differential equation whose solution is a family of straight lines that are tangents to the circle x^2+y^2=a^2 where a is a constant. The Attempt at a Solution So actually I'm stuck on the first part, coming up with such an equation. After some work I came up with...

Homework Statement Find a differential equation whose solution is a family of circles with centers in the xy-plane and of variable radii. Hint: Write the equation of the family as x^2+y^2-2ax-2by+2c=0 Homework Equations The previous questions asks to find a differential equation whose...

Aha! Thank you micromass. I figured I was doing something like that. However, after doing what Dick suggested, the problem became incredibly simple, and I find it rather hilarious that I didn't try doing that earlier.

Homework Statement "Determine whether the equations on the right define implicit functions of x. For those which do, determine whether they are implicit solutions of the differential equations on the left." e^(x-y) + e^(y-x)(dy/dx) = 0, e^(2y)+e^(2x) = 1 The Attempt at a Solution Apologies...

Aha. That clears things up. Thanks!

(Apologies for ascii art math, I don't know latex. Also apologies if this is in the wrong forum.) Homework Statement Why, in this lemma, must there be a vector v in V? That is, why must V be nonempty? An isomorphism maps a zero vector to a zero vector. Where f:V->W is an isomorphism, fix any...