%% %% 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 2.3 of the free and open-source %% LaTeX package "mathfont," released September 2023, to be used %% with the XeTeX or LuaTeX engines. (As of version 2.0, LuaTeX %% is recommended.) %% %% Copyright 2018-2023 by Conrad Kosowsky %% %% This Work may be used, 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. %% %% PLEASE KNOW THAT THIS FREE SOFTWARE IS PROVIDED WITHOUT %% ANY WARRANTY. SPECIFICALLY, THE "NO WARRANTY" SECTION OF %% THE LATEX PROJECT PUBLIC LICENSE STATES THE FOLLOWING: %% %% THERE IS NO WARRANTY FOR THE WORK. EXCEPT WHEN OTHERWISE %% STATED IN WRITING, THE COPYRIGHT HOLDER PROVIDES THE WORK %% `AS IS’, WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED %% OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED %% WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR %% PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE %% OF THE WORK IS WITH YOU. SHOULD THE WORK PROVE DEFECTIVE, %% YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR, OR %% CORRECTION. %% %% IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED %% TO IN WRITING WILL THE COPYRIGHT HOLDER, OR ANY AUTHOR %% NAMED IN THE COMPONENTS OF THE WORK, OR ANY OTHER PARTY %% WHO MAY DISTRIBUTE AND/OR MODIFY THE WORK AS PERMITTED %% ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, %% SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT %% OF ANY USE OF THE WORK OR OUT OF INABILITY TO USE THE WORK %% (INCLUDING, BUT NOT LIMITED TO, LOSS OF DATA, DATA BEING %% RENDERED INACCURATE, OR LOSSES SUSTAINED BY ANYONE AS A %% RESULT OF ANY FAILURE OF THE WORK TO OPERATE WITH ANY %% OTHER PROGRAMS), EVEN IF THE COPYRIGHT HOLDER OR SAID %% AUTHOR OR SAID OTHER PARTY HAS BEEN ADVISED OF THE %% POSSIBILITY OF SUCH DAMAGES. %% %% For more information, see 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 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'.