Recent content by Gavins

Thanks. So doing what you've said, f(a) = \frac{1}{2\pi i} \int_{\partial D} \frac{f(z)}{z -a}dz = \frac{1}{2\pi i} \int_0^{2\pi} \frac{f(a + Re^{i\theta})}{Re^{i\theta}} iRe^{i\theta} d\theta = \frac{1}{2\pi} \int_0^{2\pi} f(a + Re^{i\theta}) d\theta where I have parametrised the contour as...

Homework Statement Suppose f is a holomorphic function on U = C - {0} and that | f(z) | \leq | z |^{\frac{1}{2}} for all z in U. Show that f is everywhere zero.Homework Equations That question is supposed to require Cauchy's Integral Formula.The Attempt at a Solution Choose R>0 and take points...

Hey I am studying electromagnetism at the moment and one problem I'm having is the energy density. Instead of typing everything out, this pdf has everything. http://www.physics.sfsu.edu/~lea/courses/ugrad/360notes11.pdf There are some things I don't understand. Why is the surface integral 0...

I'm not sure I understand. Is this easy to do from first principles? I think that's what my lecturer wants. Specifically, using the definition of the derivative, f(x+h) = f(x) + f'(x)h + p(h). Thanks.

You're pretty close. Find the distance between the two walkers which is the integral you have. Evaluate that for some t. Then you can differentiate and set to zero to find the maximum.

f'(A)A + f(A) = 0? f'(A) = -A^-2 That's assuming the derivative exists. Check if the remainder term goes to 0 to show it is differentiable. Let |.| be the norm. (A + H)^-1 - A^-1 + A^-2H = p(H) |p(H)|/|H| = |(A + H)^-1 - A^-1 + A^-2H|/|H| =< |(A+H)^-1|/|H| - |A^-1|/|H| + |A^-2| I...

Homework Statement Let f: R^nxn -> R^nxn be the function f(A) = A^-1. ie f is the inverse function for some nxn matrix. Show it is differentiable and find the derivative. Homework Equations The Attempt at a Solution I need to do something along the lines of (A + H)^-1 = A^-1 +...

Have you tried anything yet? Induction has some very clear steps. First, show it is true for n=1. Then assume n=k is true and see what happens with k+1.

Use row operations to bring the matrix to diagonal form. The determinant is the sum of the diagonals. Also, remember what the operations do to the determinant. Multiplying any row by a constant multiplies the determinant by a constant. Exchanging rows makes the determinant negative. Adding rows...

Ah, I'm an idiot. I don't know how epslatex works but I've figured it now. One quick question, how do you put in the plus or minus symbol into titles/labels?

Yes, that is right.

Hey guys, I am trying to plot some graphs to use in LaTeX. In gnuplot, I run the command set term epslatex set output "graph.tex" plot ... However, my graph is blank. The axis and grid are there but text and curves are missing. If I set the terminal to aquaterm or X11, they look perfet...

The sine function is bounded. -1 \leq sin(1/x) \leq 1 Now incorporate g(x).

Have you tried the squeeze theorem?

Hm.. That's pretty bad since I found this on an final exam paper a few years back. Thanks anyway. I'm glad that it wasn't me who was wrong.