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-\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}