%% %% This is file `mathfont_equations.tex', %% generated with the docstrip utility. %% %% The original source files were: %% %% mathfont_code.dtx (with options: `equations') %% %% This file is from version 2.0 of the free and open-source %% LaTeX package "mathfont," to be used with the XeTeX or %% LuaTeX engines. (As of version 2.0, LuaTeX is recommended.) %% %% Copyright 2018-2021 by Conrad Kosowsky %% %% This file may be distributed and modified under the terms %% of the LaTeX Public Project License, version 1.3c or any %% later version. The most recent version of this license is %% available online at %% %% https://www.latex-project.org/lppl/. %% %% This Work has the LPPL status "maintained," and the current %% maintainer is the package author, Conrad Kosowsky. He can %% be reached at kosowsky.latex@gmail.com. %% %% THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT ANY EXPRESS %% OR IMPLIED WARRANTY, INCLUDING THE IMPLIED WARRANTIES %% OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. %% IF THE SOFTWARE IS DEFECTIVE, YOU AGREE TO ASSUME THE %% COST FOR ANY REPAIR OR CORRECTION. %% %% BY USING OR DISTRIBUTING THIS SOFTWARE, YOU AGREE %% TO RELEASE THE PACKAGE AUTHOR FROM ANY LIABILITY FOR %% DAMAGES ARISING OUT OF YOUR USE OF THE SOFTWARE. YOU %% AGREE TO DO SO TO THE MAXIMUM EXTENT ALLOWED UNDER %% APPLICABLE LAW AND EVEN IF THE PACKAGE AUTHOR HAS %% BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. %% %% See also the "No Warranty" section of the LaTeX Project %% Public License. In releasing the package author from %% liability, you also release from liability any third %% parties who distribute the software under the terms %% of the LaTeX Project Public License. Derivative works %% based on this package may come with their own license or %% terms of use, and the package author is not responsible %% for any third-party software. %% %% For more information, see the mathfont_code.dtx. %% %% Happy TeXing! %% \begin{multicols}{2} \let\medskip\relax Black-Scholes Equation \[ \frac{\partial V}{\partial t}+\frac12\sigma^2S^2\frac{\partial^2V}{\partial S^2}= rV-rS\frac{\partial V}{\partial X} \] \medskip 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*} \medskip Einstein's Field Equation (General Relativity) \[ R_{\mu\nu}-\frac12Rg_{\mu\nu}+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu} \] \medskip First Isomorphism Theorem \[ \phi(X)\cong X/\ker(\phi) \] \medskip Gauss-Bonnet Formula \[ \int_MK\ dA+\int_{\partial M}k_g\ ds=2\pi\chi(M) \] \medskip 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*} \medskip Michaelis-Menten Model \[ v=\frac{d[P]}{dt}=V\frac{[S]}{K_M+[S]} \] %% 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*} \medskip Quadratic Formula \[ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \] \medskip Ramanujan's Approximation for $\Gamma$ \[ \Gamma(1+x)\approx\sqrt\pi\,x^xe^{-x}\,\sqrt[6]{8x^3+4x^2+x+\frac1{30}} \] \medskip Residue Theorem \[ \frac1{2i\pi}\int_{\gamma}f(z)\ dz=\sum_{k=1}^n\Res_{a_k}(f) \] \medskip 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*} \medskip Schrodinger Equation \[ i\hbar\frac d{dt}|\Psi(t)\fakerangle=\hat H|\Psi(t)\fakerangle \] \medskip Lorentz Transformation (Special Relativity) \[ t'=\left(t-\frac{vx}{c^2}\right)\frac1{\sqrt{1-\frac{v^2}{c^2}}} \] \end{multicols} \endinput %% %% End of file `mathfont_equations.tex'.