EZ4BYG 🌍

Logarithm base e: \ln x 1$ \ln x $ \ln x Logarithm base 10: \lg x 1$ \lg x $ \lg x Logarithm base a: \log_a x 1$ \log_a x $ \log_a x

Basic grammar using matrix in Markdown12345678910$$\left( \begin{matrix} a & b & c & d & e \\ f & g & h & i & j \\ k & l & m & n & o \\ p & q & r & s & t \end{matrix}\right) $$ \begin{pmatrix} a & b & c & d & e \\ f & g & h & i & j\\ k & l & m & n & o\\ p & q & r & s & t \end{pmatrix} Matrix equation with color 1234567891011121314151617181920212223242526272829303132$$\left\{ \begin{m ...

Sum: \sum_{0}^{2} or \sum\limits_{0}^{2} 12$\sum_{0}^{2}$$\sum\limits_{0}^{2}$ \sum_{0}^{2} Integral: \int_{x}^{2} or \int\limits_{x}^{2} 12$\int_{x}^{2}$$\int\limits_{x}^{2}$ \int_{x}^{2} Note: When you need in-line formulas, the \sum_{0}^{2} is $\sum_{0}^{2}$, but the \sum\limits_{0}^{2} is $\sum\limits_{0}^{2}$.

Signs for Differentials And Derivatives are commonly used in daily work, so I put them together as follows Differential / Derivative 1: \partial x 12$ \frac{\partial f}{\partial x} $ % first order$ \frac{\partial ^{n} f}{\partial x^{n}} $ % nth order \frac{\partial f}{\partial x} \quad \frac{\partial ^{n} f}{\partial x^{n}} Differential / Derivative 2: \mathrm{d} x 12$ \frac{\mathrm{d} y }{\mathrm{d& ...

The Norm: \parallel x \parallel 1$ \parallel x \parallel $ \parallel x \parallel Two-way arrow: \rightleftharpoons 1$ \rightleftharpoons $ \rightleftharpoons

In equation environment, we can add color and background color to symbols color: \$Y = {\color{red}{5}}x\$Y = {\color{red}{5}}x background color: \$Y = \colorbox{red}{5}x\$Y = \colorbox{red}{5}x Note: Adding color needs the outermost pair of curly brackets, but adding background color doesn’t need.

We can directly type Roman Numbers and Capital Roman Numbers without using any package. Roman Numbers command: \romannumeral + num Capital Roman Numbers command: \uppercase\expandafter{\romannumeral + num} For example 123456789Some Roman Numbers: \romannumeral1, \romannumeral3, \romannumeral6.Some Capital Roman Numbers: \uppercase\expandafter{\romannumeral1}, \uppercase\expandafter{\romannumeral3}, \uppercase\expandafter{\romannumeral6}. The result

Small CapsAll caps should be in function environment ^ cap: \$\hat{x}\$\hat{x} ~ cap: \$\tilde{x}\$ \tilde{x} inverted triangle cap 1: \$\check{x}\$ \check{x} inverted triangle cap 1: \$\breve{x}\$ \breve{x} tone cap 1: \$\grave{x}\$ \grave{x} tone cap 2: \$\acute{x}\$ \acute{x} Big Caps ^ big cap: \$\widehat{abcdefg}\$ \widehat{abcdefg} ~ big cap: \$\widetilde{abcdefg}\$ \widetilde{abcdefg}

The basic piecewise function in Markdown / LaTeX is using ‘cases’ environment: 12345$$ Function = \begin{cases}Formula1 & Condition1 \\Formula2 & Condition2 \\Formula3 & Condition3 \end{cases}$$ For example: 1234567$$ (T_m,T_n) = \int_{-1}^{1}\frac{T_m(x)T_n(x)}{\sqrt {1-x^{2}}}dx = \begin{cases}0 & if m ≠ n \\\pi & if m = n =0 \\\frac{\pi}{2} & if m = n ≠ 0\end&# ...

In LaTeX, ~ is used for other purpose, so it need to be typed in special ways. We have two ways: In Text environemnt: \textasciitilde In Formula environment: $\sim$ Note: the second one is larger than the first one.