.4 sec Latency

This was taken a few nights ago. I used mjpg-streamer over wireless at 10fps.

New Equations!

Homework for chapter 10 is done!

The follow equations were used, along with some for Dr. M. Smith, Professional Bad-Ass Calc professor.

Here is the rendering!



Here is the LaTeX.

\begin{enumerate}
\item $\psi (r,\theta, \phi) = \frac{1}{\sqrt{\pi}} \left ( {}\frac {1}{a_{0}} \right )^{3/2} e^{-r/a_{0}}$ \\
\item $\left | \psi (r) \right |^{2} 4\pi r^{2} dr$ \\
\item $P(r) = 4a_{0}^{-3}\int_{0}^{\infty} r^{2}e^{-2r/a_{0}}dr$ \\
\item $4 \pi r^{2}$ \\
\item $-\frac {\hbar ^{2}}{2m} \nabla^{2} \psi (\mathbf{r}) \hspace{6pt} + \hspace{6pt} U(\mathbf{r})\psi (\mathbf{r}) \hspace{pt6} = \hspace{6pt} E\psi(\mathbf{r})$ \\
\item $ -\frac {\hbar ^{2}}{2m} \nabla^{2} \psi (\mathbf{r}) \hspace{6pt} + \hspace{6pt} U(\mathbf{r})\psi (\mathbf{r}) \hspace{6pt} = \hspace{6pt} E\psi(\mathbf{r}) $ \\
\item $\nabla^{2} = \frac{\partial^2 }{\partial r^2} +\left ( \frac {2}{r} \right )\frac{\partial }{\partial r} +\frac{1}{r^{2}} \left [\frac{\partial^2 }{\partial \theta^2} +cot \theta \frac{\partial }{\partial
\theta}+ csc^{2}\theta \frac{\partial^2 }{\partial \phi^2} \right ] $ \\
\item $\nabla^{2} = \frac{\partial^2 }{\partial x^2} + \frac{\partial^2 }{\partial y^2} + \frac{\partial^2 }{\partial z^2} $ \\
\item $ \frac{\mathrm{d} }{\mathrm{d} v} n(v)dv = \frac{4\piN}{V}\left ( \frac{m}{2\pi K_{B}T} \right )^{\frac{3}{2}} \left \{ 2ve^ {\frac{-mv^{2}}{2K_{B}T}}+\frac{-2m}{2K_{B}T}v^{3}e^ {\frac{-mv^{2}}{2K_{B}T}}\right \}$ \\
\item $ $ \\
\item $ $ \\


\end{enumerate}

LaTeX Equations from tonight

The following images are LaTeX generated and I made them in the process of doing my homework. They serve here as a reminder of syntax, nostalgia-bait, and examples of the power/shortcomings of LaTeX. Also, check out SAGE.

Equations
Code:

\documentclass[a4paper,10pt]{scrartcl}
\usepackage[utf8x]{inputenc}

%opening
\title{10.8 Feb 4}
\author{Spencer Krum}

\begin{document}

\maketitle

\begin{abstract}

\end{abstract}

\section{Equations}
\begin{enumerate}
\item $v_{mp} = \sqrt{\frac{2k_{b}T}{m}}$
\item $n(v)dv = \frac{4 \pi N}{V}\left ( \frac{m}{2\pik_{b}T} \right )^{3/2}v^{2}e^{\frac{-mv^{2}}{2k_{b}T}}dv$
\item $-4 \, \frac{\pi N k m t x^{3} e^{\left(-\frac{1}{2} \, k m t x^{2}\right)}}{V} + 8 \, \frac{\pi N x e^{\left(-\frac{1}{2} \, k m t x^{2}\right)}}{V}$
\item $-c k m t x^{3} e^{\left(-\frac{1}{2} \, k m t x^{2}\right)} + 2 \, c x e^{\left(-\frac{1}{2} \, k m t x^{2}\right)}$

\end{enumerate}


\end{document}

Statistical Physics

There are 3 important distributions you should know about. This information may one day save your life.

1) Maxwell-Boltzman distribution.
2) Bose-Einstein distribution.
3) Fermi-Dirac Distribution.

You use these when you want to deal with an ensemble of particles. Not one electron around a hydrogen nucleus but moles of electrons on the surface of a conducting sphere. These distributions have differences in how and when you use them but the all do essentially the same thing for you: They describe the energy states of particles as a function of temperature. Do note the difference between temperature and heat as it is a significant one in thermodynamics.