Recent content by murmillo

That's not what I got. Could you show your work?

Here are some comments that I think will help: -Sqrt [1 - y^2] and Sqrt [1 - y^2] are in terms of x, so if you were integrating with these bounds you would be integrating with respect to x, not y. If you had an equation and you integrated it from -Sqrt{1-y^2] to Sqrt[1-y^2], you would end up...

Homework Statement Show that every conformal self-map of the complex plane C has the form f(z) = az + b, where a ≠ 0. (Hint: The isolated singularity of f(z) at ∞ must be a simple pole.) Homework Equations The Attempt at a Solution I know about conformal self-maps of the open unit...

Hi, I'm about to apply to math PhD programs and on some of the websites I can't tell whether professors are accepting students or not. Would it be appropriate for me to e-mail them and ask? It seems totally reasonable to me, but I thought I would ask anyway.

I'm not sure what you mean by the square of a column vector...

There are probably semi-colons to distinguish between the four different dimensions. So x(t) = t^2 cos(t), y(t) = t^2 sint, etc.

Yes, I agree with you. I think there's a typo somewhere.

I'm not sure what you mean by Fx(Q) * 1 + Fy(Q) * -1. Are you differentiating F(Q) with respect to x and to y?

What are R, r, and h?

For f(0) it's -sin(-pi/4) = - (-sqrt2 / 2) = sqrt2 / 2 = 1/sqrt2 Could you show your work for how you got f'(x) for #2?

For the first part, it doesn't look like you used the fact that a and b have the same order... That might be a problem. Also, it's not true that the subgroup generated by b is contained in the subgroup generated by b^m. It should go the other way.

Did you try integrating with respect to y first?

The short answer to your question is no, there's no faster way. I'm tired too, so I'm assuming that you calculated the gradient correctly. You can make the denominators the same and get that the gradient is y^3 i + x^3 j. Find x and y so that the length of the gradient vector is more than sqrt 2.

By the way, don't worry if you're finding this difficult. I struggled too when I took linear algebra. There's so much that's new about it. I mean, you don't really work with numbers anymore, the concepts are quite abstract, and you're not used to "defining" addition in a way that's not the...

I see the problem. So, the way they defined addition in 5b is: the sum of any two vectors is the first vector. Always. That's the important part that I think you are not getting.