Recent content by castusalbuscor

Homework Statement The rate of evaporation of a spherical drop of liquid is proportional to its surface area. Derive R(t) assuming constant density, where R(t) is the radius of the drop as a function of time. Homework Equations I know that the surface area of the sphere is A = 4 \pi...

This was actually brought up in class the the professor shot it down, he also shot down expanding it in a Taylor series (since we need to know the derivative for it to work). The limit definition might be more appropriate. ^_^ Thanks! I wonder is there a geometric way to prove it?

So its pretty much common knowledge that: \frac{d}{dx}\sin (x) = \cos (x) But how does one go about to actually prove it? This came up in my Math Methods class while we were talking about Bessel Functions.

Homework Statement The problem is to integrate: \oint_{C}\frac{dz}{z^{2}-1} C is a C.C.W circle |z| = 2. Homework Equations The Attempt at a Solution I used the Cauchy integral formula: \oint_{C}\frac{f(z)}{(z-z_{0})^{n+1}}dz = \frac{2 \pi i}{n!}f^{n}(z_{0}) Which...

Yeah, I just tried it and it did not work. using cout << complex<double>(1,5) does indeed output (1,5). However, when I use complex<double> a; a = complex<double>(1,5); cout << a; I get (5,0). And when I use std::cout << (1, 5) << std::endl I still get (5,0)

Hi, I've been trying to write a program to solve a propagation of a wave packet using the time dependent Schrödinger equation. and I noticed I would need to use complex numbers. I know that I need to use #include<complex> I declare my array, and I started with a simple 1-d array...

Solved? I ended up going with \frac{1}{\pi}\left( \frac{sin((n-5)x}{32(n-5)} - \frac{sin((n+5)x}{32(n+5)} - \frac{5sin((n-3)x}{32(n-3)} + \frac{5sin((n-1)x}{16(n-1)} - \frac{5sin((n+1)x}{16(n+1)} \right)^{\pi}_{-\pi} and I just plugged in \pi and -\pi. I talked to one of the "smart"...

Homework Statement So I have to find the Fourier series for sin^{5}(x). Homework Equations I know the a_{n} in: \frac{a_{0}}{2} + \sum^{\infty}_{n=1}a_{n}cos_{n}x + \sum^{\infty}_{n=1}b_{n}sin_{n}x goes to zero, which leaves me with taking the b_{n}. The Attempt at a Solution So what I got...

Sounds doable.. will. report back with success or failure.

I've never used Mathematica, though there seems to be a lot of people mentioning it. The prof wants us to use either C/C++ or FORTRAN. I have some experience with C++ so that's what I would be using. Also I would be compiling it in Unix/Linux, if that helps... Found an equation on Wikipedia...

So for an assignment I have to write a program to find the roots of the Neumann function N_{n}(x). However the only Neumann function I have in my class notes is: Which is not overly helpful, and its the only one that was "boxed" in class. Any hints on how I can incorporate that into a...

I have a project to work on that's due by mid March. I would need to write a computer program, to show how a wave packet reflect off a barrier? How much of the wave reflects off a wall of finite height and thickness, and how much tunnels through? I remember doing something similar in my...

So today I was bouncing some ideas off one of the smart kids in my class, and was asking for some direction. The way he suggested I approach it was through density. The big arse integral I had to integrate which give the required answer was: F = \int\frac{4GM^{2}r^{3}sin\phi cos\phi d\phi...

Yes. the solution is \frac{3M^{2}G}{4a^{2}}

[SOLVED] Forece Between Two Hemispheres I am trying to study for my classical mechanics final, and the prof hinted that this problem would be on the final. Two uniform rigid hemispheres eachof mass M and radius a are placed in contact with each other so as to form a complete sphere. Find the...