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\begin{document}
Date 02/01/13 with {\bf corrections} where vector printout
does not match postscript file.
\vs

\noindent{A. \it Einstein mass/energy:} 

$$E_0 = mc^2$$
\vs

\noindent{B. \it Maxwell's Equations in Vacuum:}

{\bf correction: minus sign in front of fraction, not in numerator}
 
$$\begin{array}{l}
\nabla \cdot {\bf B}  = 0 \\
\nabla \times {\bf B}  = \frac{\ds 1}{\ds c}\frac {\ds \partial {\bf E}}
{\ds \partial t}\\
\end{array}~~~~~
\begin{array}{l}
\nabla \cdot {\bf E}  = 0 \\
\nabla \times {\bf E}  = -\frac{\ds 1}{\ds c}\frac{\ds \partial {\bf B}}
{\ds \partial t}\\
\end{array}$$
\vs 

\noindent{C. \it Stokes' Theorem}
$$\int_{M}d\omega=\int_{\partial M}\omega$$
\vs

\noindent{D. \it }
$$\{Q,Q\} = P$$
\vs

\noindent{E. \it Primes and the zeta function:} 
$$ \sum_{n=1}^{\infty}\frac{1}{n^s} = \prod_p \frac{1}{1-\frac{1}{p^s}} $$ 

\vs

\noindent{F. \it Heisenberg Uncertainty Principle:}
$$\Delta x \Delta p \geq  \hbar/2$$
\vs

\noindent{G. \it Kepler's Second Law} 

$$\frac{d\theta}{dt} \propto \frac{1}{r^2}$$
\vs
\newpage

\noindent{H. \it Kepler's Third Law} 

$$ T^2 \propto a^3$$
\vs

\noindent{I. \it Newton's Law of Gravitation:}
$$ F = \frac{\ds G m_1m_2}{\ds r^2}$$
\vs

\noindent{J. \it Newton's Law} \vs

$${\bf F} = m {\bf a}$$
\vs

\noindent{K. \it Einstein's General Relativity Equation: }
$$R_{\mu\nu}-\frac{1}{2}R g_{\mu\nu}  = 8 \pi G T_{\mu\nu}$$
\vs


\noindent{L \it Schr\"{o}dinger's Equation:}
$$ i\hbar \frac{\ds \partial\psi}{\ds \partial t} = 
-\frac{\ds \hbar^2}{\ds 2m} \nabla^2\psi + V\psi$$
\vs

\noindent{M. \it Dirac Equation:}


$$
\left(i\DDirac - m\right)  \psi=0
$$
\vs

\noindent{N. \it Atiyah-Singer Theorem for Twisted Dirac Operator:} 

%$$\Dirac :  \Gamma ({\mathbb S}_+\otimes E) \to \Gamma ({\mathbb S}_-\otimes E)$$

$$\dim \ker \slash \! \! \! \! {D}_E - \dim \mbox{coker}~  
\slash \! \! \! \! {D}_E = \int_M \hat{A}(M) \cdot ch (E)$$
\vs
\newpage

\noindent{O. \it Yang-Mills equations:}

{\bf correction: subscript A on first F}

{\bf correction close up gaps between} $A$, $\wedge$, $A$

$$F_A = dA + A \wedge A$$

$$D_A^*F_A = 0$$
\vs

\noindent{Q. \it boundary-boundary:}
$$\partial\partial = 0$$

\end{document}

