Recent content by Darth Frodo

Homework Statement Determine the location and type of singularity of f(z) = 1/sin^2(z) Homework EquationsThe Attempt at a Solution I'm not really sure how to calculate this. At this point, we don't have explicit formulae for the coefficients of a Laurent series so I really don't know what to...

Hi All, I was reading through Kreyzeig's Advanced Engineering Mathematics and came across two theorems in Complex Analysis. Theorem 1: Let f(z) = u(x,y) + iv(x,y) be defined and continuous in some neighborhood of a point z = x+iy and differentiable at z itself. Then, at that point, the...

So this is what I have so far. x_0 = r r is a non-zero real number x_{n+1} = x_n(\frac{1}{2} + \frac{c}{2x_n^2}) Case 1: ##r^2 < c~ \Rightarrow## sequence is increasing Case 2: ##r^2 > c ~\Rightarrow## sequence is decreasing

So, I have an idea, but I'm not sure if it proves convergence. If x_{n} = g(x_{n-1}) then all I have to do it let x = g(x).EDIT: Upon further thought, it does not as convergence => x_{n} = g(x_{n-1}). It is not a iff situation. Back at square one.

Homework Statement Prove for c>0 the sequence {x_n} = \frac{1}{2}(x_{n-1} + \frac{c}{x_{n-1}}) converges. The Attempt at a Solution This is proving difficult, I have never dealt with recursive sequences before. Any help would be appreciated. Thanks.

Hey guys, In a bit of a sticky situation here. So, there is a prof. who wants me to work with him over the summer and then into the future, the issue is, his area of research is NOT what I see myself doing or even interesting. My question is, how would you tell him that you would rather...

If micromass were here he'd most likely recommend: https://www.physicsforums.com/showthread.php?t=665174

Homework Statement A stone is thrown with a velocity v_{0} at an angle \alpha to the horizontal (see image) from a step of height H. Calculate the x coordinate x_{1} of the point where the stone hits the ground. Homework Equations x(t) = u_{x}t + x_{0} y(t) = u_{y}t +...

Hi all, I am taking a Numerical Computation course this year which basically consists of learning MATLAB and R. We are tasked with doing a mini research project which involves using either of theses environments. I am most interested in classical mechanics and have recently taken a course in...

My schedule this semester in order of eagerness to study. Theoretical Mechanics. Partial Differential Equations. Operations Research. Numerical Analysis. Numerical Computation (MatLab).

One thing that really helps me calm my nerves during a test is to go through it methodically. I do this by: 1. Assuming that I am an average or above average student with regards to time required to take the test. Therefore, I do not have to worrry about time as longa s I go at my own (typical)...

Oh ok. Thanks Mark & phinds! That really cleared it up!

When is it appropriate to use \equiv as opposed to =?

Moment Generating Function and Expected Value of the Continuous random variable X

Continuous Uniform MGF is M_{x}(z) = E(e^zx) = \frac{e^{zb} - e^{za}}{zb - za} \frac{d}{dz}M_{x}(z) = E(X) Using the Product Rule \ U = e^{bz} - e^{az} \ V = (zb - za)^{-1} \ U' = be^{bz} - ae^{az} \ V' = -1(zb - za)^{-2}(b - a) \frac{dM}{dz} = UV' + VU' \frac{dM}{dz}...