Recent content by upsidedowntop

deRham, It looks like we have a second vote for the opinion: "If you don't want to do research, don't pursue a PhD." Like I told Micromass, I'll keep your comment in mind while I make the decision. "I'm confused what is meant by \"grad school\" - if it's in CS or mathematics, often there...

Wow, Thanks everyone. There is a lot of good advice here. I'll respond to each of you, but will refrain from quoting people since that would make for a ridiculously long post. Micromass, I'll remember your comment when I make the decision whether or not to go to grade school. Research is...

You don't need to give WA the correct formulas with which to evaluate an integral... "int from 0 to 1 (1-x^2)^4" returns 128/315 See: http://www.wolframalpha.com/input/?i=int+from+0+to+1+(1-x^2)^4 It will do infinite sums, limits and derivatives too. I find it really useful for checking work.

Ah, forgive my first post. The bearing in the first part is the direction of travel of the enemy, not the direction of the enemy relative to the airbase. I have a suggestion then. Suppose the interceptor intersects the enemies line of travel at the exact same time that the enemy reaches the...

Yes, that's right. I'm sorry, I brought it up. It's a common mistake for people to think that the slash in the symbol for derivatives or the Jacobian is a division sign. So, when you called the symbol for the Jacobian a formula, I thought you were taking that mistake. Sorry for jumping to...

|d(u,v) / d(x,y)| is the notation for the Jacobian. Does d(x,y) mean anything to you, other than the top part of the symbol for the Jacobian? The "formula" or definition of the Jacobian of a transformation f: R^n \rightarrow R^n is as follows. The Jacobian is the determinant of the...

It seems to me that there is incomplete information to answer the question. You need to know what time the first observation (that the enemy was at 40 degrees) was made at. Or you need to know how far away it was when the observation was made. But, as is, there is no was to figure out the...

Two more comments: You need one more property of power series to answer these questions: f(x) = \sum a_n x^n \Rightarrow f(x)x^m = \sum a_n x^{n+m} I would feel bad about giving so many suggestions, except the 4 properties of power series I mentioned are properties you wouldn't be able...

I'm not sure what you have been asked to do, but the following properties of power series might help you anyway. \frac{1}{1-x} = \sum x^n f(x) = \sum a_n x^n \Rightarrow f'(x) = \sum na_n x^{n-1} f(x) = \sum a_n x^n \Rightarrow \int^x f(x) = \sum \frac{a_n}{n+1} x^{n+1}...

\lambda A^{-1} mapping all eigenvectors of A to themselves does not imply \lambda A^{-1} = I.

The function for the height of the dome at a given (x,y) is going to have to be piece wise because at some points it's the first cylinder and at some points the second cylinder. That's probably why you're having trouble finding the function to integrate. My advice is to split the xy-plane into...

My advice is to choose based on what sort of math you like more. Quantum uses a lot of linear algebra, differential equations, probability, and a little abstract algebra. Electromagnetism is much more similar to mechanics than quantum is. It relies more on vector calculus and...

I get: \int_0^1 (1 - x^2)^4 dx = \frac{8}{9}\frac{6}{7}\frac{4}{5}\frac{2}{3}\int_0^1 1 dx So the answer is: \frac{(8)(6)(4)(2)}{(9)(7)(5)(3)} = \frac{2^7}{(3^2)(5)(7)} = \frac{128}{315} Wolframe Alpha agrees with the above answer.

Hi, I'm looking for general advice on quite a few topics related to grad school. I'll give you some background information and then ask the questions which I've been having trouble reaching conclusions about. I am a senior at MIT majoring in math with computer science. During Sophomore...

Thanks a lot everyone, this was really helpful. Regarding the question I just asked, which Sammy just answered, thanks. I was asking myself what function \displaystyle \sum_{k=0}^\infty\frac{x^{k+1}}{k!} was a power series for, but for some reason it wasn't clicking. I guess I'm pretty...