Date 02/01/13 with corrections where vector printout does not match postscript file.

A. Einstein mass/energy:

E_{0} = mc^{2}

B. Maxwell’s Equations in Vacuum: correction: minus sign in front of fraction, not in numerator

\begin{matrix}∇ · B = 0 \\ ∇ × B = \frac{1}{c} \frac{∂E}{∂t} \end{matrix} \begin{matrix}∇ · E = 0 \\ ∇ × E = −\frac{1}{c} \frac{∂B}{∂t} \end{matrix}

C. Stokes’ Theorem

∫_{M} dω = ∫_{∂M} ω

D.

{Q, Q} = P

E. Primes and the zeta function:

∑_{n=1}^{∞} \frac{1}{n^{s}} = ∏_{p} \frac{1}{1 − \frac{1}{p^{s}}}

F. Heisenberg Uncertainty Principle:

ΔxΔp ≥ ℏ/2

G. Kepler’s Second Law

\frac{dθ}{dt} ∝ \frac{1}{r^{2}}

H. Kepler’s Third Law

T^{2} ∝ a^{3}

I. Newton’s Law of Gravitation:

F = \frac{Gm_{1}m_{2}}{r^{2}}

J. Newton’s Law

F = ma

K. Einstein’s General Relativity Equation:

R_{μν} − \frac{1}{2}Rg_{μν} = 8πGT_{μν}

L Schrödinger’s Equation:

iℏ\frac{∂ψ}{∂t} = −\frac{ℏ^{2}}{2m}∇^{2}ψ + V ψ

M. Dirac Equation:

(i D̸ − m) ψ = 0

N. Atiyah-Singer Theorem for Twisted Dirac Operator:

dim ker / D_{E} − dim coker / D_{E} = ∫_{M} Â(M) · ch(E)

O. Yang-Mills equations: correction: subscript A on first F correction close up gaps between A, ∧, A

F_{A} = dA + A ∧ A
D_{A}^{∗}F_{A} = 0

Q. boundary-boundary: ∂∂ = 0