added Latex examples

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jkriege2 2022-06-08 15:38:55 +02:00
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commit 993ed1fb3d
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/.vs
/CMakeSettings.json
/out
*.synctex.gz

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\item\textbf{Schrödinger's equation:} \[\left[-\frac{\hbar^2}{-2m}\frac{\partial^2}{\partial x^2}+V\right]\Psi(x)=i\hbar\frac{\partial}{\partial t}\Psi(x) \]
\item\textbf{Cauchy-Schwarz inequality:} \[\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
\item\textbf{Maxwell's equations:} \[\begin{aligned}\nabla \times \vec{\mathbf{B}} -\, \frac{1}{c}\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\nabla \times \vec{\mathbf{E}}\, +\, \frac{1}{c}\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} \]
\item\textbf{math: radicals:} \[\sqrt{a}\sqrt{5}\sqrt{-1}\sqrt{h}\sqrt{jA}\sqrt{\vec{A}}\sqrt{\frac{1}{a}}\frac{\sqrt{a}}{\sqrt{a}}\sqrt{\frac{1}{1+\frac{1}{a}}}\frac{1}{\sqrt{1+\frac{1}{a}}}\sqrt{a+\sqrt{a+b}}\]
\item\textbf{math: non-2 radicals:} \[\sqrt[3]{a}\sqrt[3]{5}\sqrt[3]{-1}\sqrt[3]{h}\sqrt[3]{\vec{A}}\sqrt[3]{\frac{1}{a}}\frac{\sqrt[3]{a}}{\sqrt[3]{a}}\sqrt[3]{\frac{1}{1+\frac{1}{a}}}\frac{1}{\sqrt[3]{1+\frac{1}{a}}}\sqrt[3]{a+\sqrt[3]{a+b}}\]
\item\textbf{math: long non-2 radicals:} \[\sqrt[3.14156]{a}\sqrt[3.14156]{5}\]
\item\textbf{math: sum, prod, ...:} no-limits: \[\prod_{i=1}^n \sum_{j=1}^c (i + j)\cdot\frac{1}{2}\]\ \ \ --\ \ \ limits: \[\prod\limits_{i=1}^n \sum\limits_{j=1}^c (i + j)\cdot\frac{1}{2}\]\ \ \ --\ \ \ long-below: \[\sum_{n=\{a,b,c,d,e,f,g\}} f(x)\]\ \ \ --\ \ \ long-above: \[\sum^{n=\{a,b,c,d,e,f,g\}} f(x)\]
\item\textbf{math: more sum-symbols :} \[\sum_{i=0}^N\prod_{i=0}^N\coprod_{i=0}^N\bigcup_{i=0}^N\bigcap_{i=0}^N\bigsqcup_{i=0}^N\bigvee_{i=0}^N\bigwedge_{i=0}^N\bigoplus_{i=0}^N\bigotimes_{i=0}^N\bigodot_{i=0}^N\biguplus_{i=0}^N\]
\item\textbf{math: integrals:} no-limits: \[\int_{0}^1 f(x)\;\mathrm{d}x\ \iint_{0}^1 f(x)\;\mathrm{d}x\ \iiint_{0}^1 f(x)\;\mathrm{d}x\ \oint_{0}^1 f(x)\;\mathrm{d}x\ \int_{x} f(x)\;\mathrm{d}x\]\ \ \ --\ \ \ limits: \[\int\limits_{0}^1 f(x)\;\mathrm{d}x\ \iint\limits_{0}^1 f(x)\;\mathrm{d}x\ \iiint\limits_{0}^1 f(x)\;\mathrm{d}x\ \oint\limits_{0}^1 f(x)\;\mathrm{d}x\ \int\limits_{x} f(x)\;\mathrm{d}x\]
\item\textbf{math: frac test:} \[\frac{a}{b}+\frac{g}{a}-\frac{a^2}{b^2}\cdot\frac{a^2}{b^{\frac{1}{2}}}\]
\end{itemize}

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