%%
%% This is file `mathfont-equations.tex',
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%% For more information, see mathfont-code.dtx. Happy TeXing!
%% 
\multicolsep=0pt\relax
\bigskip
\begin{multicols*}{2}

Black-Scholes Equation
\[
\frac{\partial V}{\partial t}+
  \frac12\sigma^2S^2\frac{\partial^2V}{\partial S^2}
  =rV-rS\frac{\partial V}{\partial X}
\]

\vfill

Cardano's Formula/Cubic Formula
\begin{align*}
t_i&=\omega_i\sqrt[3]{-\frac q2+\sqrt{\frac{q^2}4+\frac{p^3}{27}}}\\
  &\qquad\qquad{}+\omega_i^2\sqrt[3]{-\frac q2-\sqrt{\frac{q^2}4+\frac{p^3}{27}}}
\end{align*}

\vfill

Einstein's Field Equation (General Relativity)
\[
R_{\mu\nu}-\frac12Rg_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}
\]

\vfill

First Isomorphism Theorem
\[
\phi(X)\cong X/\ker(\phi)
\]

\vfill

Gauss-Bonnet Formula
\[
\int_MK\ dA+\int_{\partial M}k_g\ ds=2\pi\chi(M)
\]

\vfill

Maxwell's Equations
\begin{align*}
\nabla\bullet\mathbf E&=\frac\rho{\epsilon_0}&
\nabla\bullet\mathbf B&=0\\
\nabla\times\mathbf E&=-\frac{\partial\mathbf B}{\partial t}&
\nabla\times\mathbf B&=\mu_0\left(\mathbf J+
  \epsilon_0\frac{\partial\mathbf E}{\partial t}\right)
\end{align*}

\vfill

Michaelis-Menten Model
\bgroup
\belowdisplayskip=0pt\relax
\belowdisplayshortskip=0pt\relax
\[
v=\frac{d[P]}{dt}=V\frac{[S]}{K_M+[S]}
\]
\par\egroup
\hrule height 0pt
\columnbreak
%% next column begins here

Navier-Stokes Equation
\begin{align*}
\frac{\partial}{\partial t}(\rho\mathbf{u})+\nabla\bullet
  (\rho \mathbf{u}\otimes \mathbf{u})={}
  &{-}\nabla\bar p+\mu\nabla^2\mathbf{u}\\
  &+\frac13\mu\nabla(\nabla\bullet u)+
  \rho\mathbf{g}
\end{align*}

\vfill

Quadratic Formula
\[
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}
\]

\vfill

Ramanujan's Approximation for $\Gamma$
\[
\Gamma(1+x)\approx\sqrt\pi\,x^xe^{-x}\,\sqrt[6]{8x^3+4x^2+x+\frac1{30}}
\]

\vfill

Residue Theorem
\[
\frac1{2i\pi}\int_{\gamma}f(z)\ dz=\sum_{k=1}^n\Res_{a_k}(f)
\]

\vfill

Riemann Zeta Function
\begin{align*}
\zeta(z)&=\sum_{i=1}^\infty\frac1{z^i}
  =\frac1{\Gamma(z)}\int_0^\infty\frac{x^{z-1}}{e^x-1}\ dx\\
  &=2^z\pi^{z-1}\sin\left(\frac{\pi z}2\right)\,\Gamma(1-z)\,\zeta(1-z)
\end{align*}

\vfill

Schrodinger Equation
\[
i\hbar\frac d{dt}|\Psi(t)\fakerangle=\hat H|\Psi(t)\fakerangle
\]

\vfill

Lorentz Transformation (Special Relativity)
\belowdisplayskip=0pt\relax
\belowdisplayshortskip=0pt\relax
\[
t'=\left(t-\frac{vx}{c^2}\right)\frac1{\sqrt{1-\frac{v^2}{c^2}}}
\]
\hrule height 0pt

\end{multicols*}
\endinput
%%
%% End of file `mathfont-equations.tex'.
