\documentclass[aspectratio=169]{beamer} \usepackage{amsmath,unicode-math,physics,tensor,xeCJK,bookmark} \useoutertheme{metropolis} \useinnertheme{metropolis} \usecolortheme{metropolis} \usefonttheme{professionalfonts} \setbeamerfont{title}{size=\Large, series=\bfseries} \setbeamerfont{author}{size=\small} \setbeamerfont{date}{size=\small} \setbeamertemplate{footline}{\vspace*{0.3cm}} \makeatletter % https://tex.stackexchange.com/q/66519 \apptocmd{\beamer@@frametitle}{\only<1>{\bookmark[page=\the\c@page,level=3]{#1}}}{}{} \makeatother \unimathsetup{math-style=ISO, bold-style=ISO, mathrm=sym} \setsansfont{FiraGO}[BoldFont=* SemiBold, Numbers=Monospaced] \setmathfont{Fira Math Regular} \newCJKfontfamily\fontzhhans{Source Han Sans SC} \newCJKfontfamily\fontzhhant{Source Han Sans TC} \newCJKfontfamily\fontja{Source Han Sans} \def\ii{\symrm{i}} \def\pp{\symrm{\pi}} \title{Fira Math} \subtitle{Sans-serif font with Unicode math support} \author{Xiangdong Zeng} \date{2019/06/03\quad v0.3.2} \begin{document} \maketitle \begin{frame}{Basic examples (I)} \begin{itemize} \item Covariant derivative: \[ \nabla \symbf{X} = \tensor{X}{^\alpha_{;\beta}} \pdv{x^\alpha} \otimes \dd{x^\beta} = \qty(\tensor{X}{^\alpha_{,\beta}} + \Gamma^{\alpha}_{\beta\gamma} \, X^\gamma) \, \pdv{x^\alpha} \otimes \dd{x^\beta} \] \item Einstein's field equations: \[ G_{\mu\nu} \equiv R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} \] \item Schwarzschild metric: \[ c^2 \dd{\tau}^2 = \qty(1-\frac{r_{\mathrm{s}}}{r}) \, c^2 \dd{t}^2 - \qty(1-\frac{r_{\mathrm{s}}}{r})^{-1} \dd{r}^2 - r^2 \underbrace{\qty(\dd{\theta}^2 + \sin^2 \theta \dd{\varphi}^2)}_{\dd{\Omega}^2} \] \item Einstein--Hilbert action: \[ S = \frac{1}{2\kappa} \int R \sqrt{-g} \dd[4]{x} \] \end{itemize} \end{frame} \begin{frame}{Basic examples (II)} \begin{itemize} \item Case $n=1$ \small \[ \int_0^{\frac{\pp}{2}} \frac{\sqrt{\frac12 \sqrt{\frac{\ln^2\cos\theta}{\theta^2+\ln^2\cos\theta}} + \frac12}}% {\fourthroot{\theta^2 + \ln^2\cos\theta}} \dd{\theta} = \frac{\pp}{2\sqrt{\ln 2}} \] \item Generalization: \small\vspace{1ex} \[ \begin{cases} \smash[t]{\displaystyle R_n^- = \frac{2}{\pp} \int_0^{\pp/2} \qty(\theta^2+\ln^2\cos\theta)^{-2^{-n-1}} \sqrt{\frac12+\frac12\sqrt{\frac12+\cdots+\frac12\sqrt{ \frac{\ln^2\cos\theta}{\theta^2+\ln^2\cos\theta}}}} \dd{\theta} = (\ln 2)^{-2^{-n}}} \\[3ex] \smash[b]{\displaystyle R_n^+ = \frac{2}{\pp} \int_0^{\pp/2} \qty(\theta^2+\ln^2\cos\theta)^{2^{-n-1}} \sqrt{\frac12+\frac12\sqrt{\frac12+\cdots+\frac12\sqrt{ \frac{\ln^2\cos\theta}{\theta^2+\ln^2\cos\theta}}}} \dd{\theta} = (\ln 2)^{2^{-n}}} \end{cases} \] \end{itemize} \end{frame} \begin{frame}{Using with CJK fonts} \begin{itemize} \item {\fontzhhans 【留数定理】全纯函数 $f$ 在若尔当曲线 $\gamma$ 上的积分为:} \[ \oint_\gamma f(z) \dd{z} = 2\pp\ii \sum_{k=1}^n \Res_{z=a_k} f(z). \] \item {\fontzhhant 【留數定理】全純函數 $f$ 在若爾當曲線 $\gamma$ 上的積分為:} \[ \oint_\gamma f(z) \dd{z} = 2\pp\ii \sum_{k=1}^n \Res_{z=a_k} f(z). \] \item {\fontja 【留数定理】ジョルダン曲線 $\gamma$ に沿う正則関数 $f$ の積分は、} \[ \oint_\gamma f(z) \dd{z} = 2\pp\ii \sum_{k=1}^n \Res_{z=a_k} f(z). \] \end{itemize} \end{frame} \end{document}