Testing Markdown and LaTeX

January 24, 2025 2 minute read

Text Formatting

Here are some basic text formatting options:

Italic text or also italic
Bold text or also bold
Bold and italic or also bold and italic
~~Strikethrough text~~
Inline code

Lists

Unordered List

Item 1
Item 2
- Subitem 2.1
- Subitem 2.2
Item 3

Ordered List

First item
Second item
1. Subitem 2.1
2. Subitem 2.2
Third item

Blockquotes

This is a blockquote It can span multiple lines

And have multiple paragraphs

Code Blocks

def hello_world():
    print("Hello, world!")
    return True

# This is a comment
for i in range(3):
    hello_world()

LaTeX Equations

Here are some example equations:

Inline equation: $E = mc^2$

Display equation:

\[\begin{aligned} \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0\left(\mathbf{J} + \epsilon_0\frac{\partial \mathbf{E}}{\partial t}\right) \end{aligned}\]

A more complex example:

\[\begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} = \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix}\]

Advanced LaTeX Examples

Complex Mathematical Expressions

Integrals and Limits

Double integral with limits: $\iint_D \left( \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} \right) dx\,dy = \oint_C P\,dx + Q\,dy$

Triple integral: $\iiint_V f(x,y,z)\,dx\,dy\,dz = \lim_{n \to \infty} \sum_{i=1}^n f(x_i,y_i,z_i)\Delta V_i$
Matrices and Determinants

Matrix with brackets: $\begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}$

Determinant: $\det(A) = \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} = aei + bfg + cdh - ceg - bdi - afh$
Series and Sums

Infinite series: $\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$

Product notation: $\prod_{i=1}^{n} x_i = x_1 \times x_2 \times \cdots \times x_n$
Physics and Engineering

Maxwell’s equations: $\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0\left(\mathbf{J} + \varepsilon_0\frac{\partial \mathbf{E}}{\partial t}\right) \end{aligned}$
Probability and Statistics

Normal distribution: $f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$

Binomial coefficient: $\binom{n}{k} = \frac{n!}{k!(n-k)!}$
Complex Analysis

Cauchy’s integral formula: $f(a) = \frac{1}{2\pi i} \oint_C \frac{f(z)}{z-a}\,dz$

Residue theorem: $\oint_C f(z)\,dz = 2\pi i \sum_{k=1}^n \operatorname{Res}(f,a_k)$
Quantum Mechanics

Schrödinger equation: $i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\mathbf{r},t)\right]\Psi(\mathbf{r},t)$

Dirac notation: $\langle\psi|\hat{H}|\phi\rangle = \int_{-\infty}^{\infty} \psi^*(x)\hat{H}\phi(x)\,dx$
Differential Geometry

Christoffel symbols: $\Gamma^k_{ij} = \frac{1}{2}g^{kl}\left(\frac{\partial g_{jl}}{\partial x^i} + \frac{\partial g_{il}}{\partial x^j} - \frac{\partial g_{ij}}{\partial x^l}\right)$

Riemann curvature tensor: $R^a_{bcd} = \partial_c\Gamma^a_{bd} - \partial_d\Gamma^a_{bc} + \Gamma^e_{bd}\Gamma^a_{ce} - \Gamma^e_{bc}\Gamma^a_{de}$

Example with Explicit Dropcap

Testing an explicitly set dropcap using a div wrapper.

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Links and Images

External Links

Reference-style Links

Here’s a link to Google and another to OpenAI.

Tables

Header 1	Header 2	Header 3
Cell 1	Cell 2	Cell 3
Cell 4	Cell 5	Cell 6
Cell 7	Cell 8	Cell 9

Task Lists

Footnotes

Here’s a sentence with a footnote¹.

This post demonstrates the basic Markdown and LaTeX features supported by Jekyll with the Minimal Mistakes theme. Feel free to use this as a reference for your own posts!

This is the footnote content. ↩