Recent content by emyt

Homework Statement sum of i from i = 1 to n 1/i^2 <= 2 The Attempt at a Solution I have a solution, that for any n the sum from i to n of 1/i^2 < sum 1/i(i-1) = 1/(i-1) - 1/i .. et c but this is not inductive.. can I get any hints? thank you

where did that 1 come from in your shell method formula?

It looks better if you write this out: \int f(g(x))g'(x)dx = \int f(u) du this is the substitution formula, the dx part is adjusted by g'(x)dx to act as du so, 2x is the g'(x) part, x^4 is your f(x) part, and g(x) = x^2 -1

thanks, I was thinking about that too, but for some reason my mind strayed and thought that I would need 2n independent vectors.. I was also looking at a couple of the diagonal "if and only if" theorems. I saw a couple that might've been useful, like: T is diagonalizable if and only if the...

Homework Statement Suppose that A \in Mnxn(F) has two distinct eigenvalues \lambda_{1} and \lambda_{2} and that dim(E_{\lambda_{1}}) = n - 1. Prove that A is diagonalizable Homework Equations The Attempt at a Solution hmm, I'm not sure.. how would I start this? thanks

interesting. Thanks for your input rasmhop, I ended up dropping the course. I will wait for until my upper years before I take a serious discrete mathematics course (and until then, I'll be doing some reading on my own)

you have a point, and I will talk to my professor. Anyway, I know what you mean by how there is a lot of "guessing" in math - I have had experience with this ( guessing which theorems may be relevant for a proof.. et c). But these are guided guesses, there is more "sense" in guessing these...

Hi, I'm currently taking a seminar course , it's like a "small group" course (like a lecture as a tutorial) in mathematics. It's open for anybody, most people there actually aren't math students. It's basically a discrete math/combinatorial/"problem solving" driven course but the thing is, I...

Thanks! This is exactly the kind of thing I was looking for. Right now I'm just working from an older edition of Resnick's Physics book (3rd edition from the 70s). I was wondering if anybody had anything to say about its difficulty level? Also, there's only 1 copy in my library and it has...

I don't think that that is all there was to it. Of course, if that WERE the case - physics would be a lot "easier". But physics isn't just math, you should be able to account for anything that would be happening "in real life" and factor those considerations in your equations.. If what you say...

"you're in pretty good shape" first year physics textbooks.. Hi, I'm wondering if there were any books for which if you were able to do the problems, then you're in good shape.. For example, if you can problems from Spivak's "Calculus" book as you are in your first year, then you're in pretty...

I see that this thread is still going, I verified (by looking it up) that "going in a straight line" is really going as a geodesic. Sorry for the confusion but this stuff is out of my depth, I wasn't entirely sure what the person was talking about, that's why I posted it here thanks for the...

I'm thinking about a fourth spatial dimension. Thanks for the replies but I don't fully understand what cesiumfrog is trying to say.. Wouldn't it be like.. It seems like we are going in a straight line in 3D but we are really going in circles in 4D?

"in 4-D, the Earth orbits around the sun in a straight line" someone told me that in 4-D, the Earth actually orbits around the sun in a straight line, could someone try to explain to me how this is so? thank you

you don't only consider the case when x and y go to zero "together", but you're basically on the right track.. there are 3 cases: 1) they both tend to zero at the same time, x=y. 2) x goes to zero first or 3) y goes to zero first. so you have axes x ,y and z and so the limit exists if there...