LaTeX/KaTeX in Slidev

This skill covers rendering mathematical formulas and scientific notation in Slidev using KaTeX, a fast LaTeX math rendering library.

When to Use This Skill

• Writing mathematical equations

• Scientific presentations

• Technical documentation

• Academic content

• Physics, chemistry, or engineering formulas

Basic Syntax

Inline Math

Surround with single $ :

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ where $a \neq 0$.

Block Math

Surround with double $$ :

$$ E = mc^2 $$

Or with line breaks:

$$ \begin{aligned} f(x) &= x^2 + 2x + 1 \ &= (x + 1)^2 \end{aligned} $$

Common Mathematical Notations

Fractions

Simple: $\frac{a}{b}$

Nested: $\frac{1}{\frac{a}{b} + c}$

Display: $$\frac{x^2 + y^2}{z}$$

Exponents and Subscripts

Exponent: $x^2$, $e^{i\pi}$ Subscript: $x_1$, $a_{ij}$ Combined: $x_1^2$, $a_{ij}^{n+1}$

Square Roots

Simple: $\sqrt{x}$ N-th root: $\sqrt[n]{x}$ Complex: $\sqrt{x^2 + y^2}$

Greek Letters

Lowercase: $\alpha$, $\beta$, $\gamma$, $\delta$, $\epsilon$, $\theta$, $\lambda$, $\mu$, $\pi$, $\sigma$, $\omega$

Uppercase: $\Gamma$, $\Delta$, $\Theta$, $\Lambda$, $\Pi$, $\Sigma$, $\Omega$

Operators

Sum: $\sum_{i=1}^{n} x_i$

Product: $\prod_{i=1}^{n} x_i$

Integral: $\int_{a}^{b} f(x) , dx$

Double integral: $\iint_D f(x,y) , dA$

Limit: $\lim_{x \to \infty} f(x)$

Equations and Formulas

Famous Equations

$$ \text{Euler's Identity: } e^{i\pi} + 1 = 0 $$

$$ \text{Pythagorean: } a^2 + b^2 = c^2 $$

$$ \text{Einstein: } E = mc^2 $$

$$ \text{Schrödinger: } i\hbar\frac{\partial}{\partial t}\Psi = \hat{H}\Psi $$

Systems of Equations

$$ \begin{cases} x + y = 10 \ 2x - y = 5 \end{cases} $$

Aligned Equations

$$ \begin{aligned} (x + y)^2 &= x^2 + 2xy + y^2 \ (x - y)^2 &= x^2 - 2xy + y^2 \ (x + y)(x - y) &= x^2 - y^2 \end{aligned} $$

Matrices

$$ A = \begin{pmatrix} a & b \ c & d \end{pmatrix} $$

$$ B = \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} $$

$$ \det(A) = \begin{vmatrix} a & b \ c & d \end{vmatrix} = ad - bc $$

Mathematical Symbols

Comparison

$<$, $>$, $\leq$, $\geq$, $\neq$, $\approx$, $\equiv$, $\sim$

Logic

$\forall$ (for all), $\exists$ (exists), $\neg$ (not) $\land$ (and), $\lor$ (or), $\Rightarrow$ (implies)

Sets

$\in$ (in), $\notin$ (not in), $\subset$, $\subseteq$ $\cup$ (union), $\cap$ (intersection) $\emptyset$ (empty set), $\mathbb{R}$ (reals), $\mathbb{N}$ (naturals)

Calculus

$\frac{dy}{dx}$, $\frac{\partial f}{\partial x}$ $\nabla f$, $\nabla \cdot F$, $\nabla \times F$

Arrows

$\rightarrow$, $\leftarrow$, $\leftrightarrow$ $\Rightarrow$, $\Leftarrow$, $\Leftrightarrow$ $\mapsto$, $\to$

Advanced Features

Line Highlighting in Math

$$ {1|3|all} \begin{aligned} f(x) &= x^2 \ // Click 1 f'(x) &= 2x \ // Click 1 f''(x) &= 2 // Click 2 \end{aligned} $$

Custom Colors

$$ {\color{red} x^2} + {\color{blue} y^2} = {\color{green} z^2} $$

Boxed Formulas

$$ \boxed{E = mc^2} $$

Text in Math

$$ f(x) = \begin{cases} x & \text{if } x \geq 0 \ -x & \text{otherwise} \end{cases} $$

Chemistry Formulas

Enable mhchem extension in vite.config.ts :

import 'katex/contrib/mhchem' export default {}

Then use:

$$\ce{H2O}$$

$$\ce{2H2 + O2 -> 2H2O}$$

$$\ce{CO2 + C -> 2CO}$$

$$\ce{Hg^2+ ->[I-] HgI2 ->[I-] [Hg^{II}I4]^2-}$$

Physics Formulas

Mechanics

$$ F = ma \quad \text{(Newton's Second Law)} $$

$$ W = \int_a^b \vec{F} \cdot d\vec{s} $$

$$ KE = \frac{1}{2}mv^2 $$

Electromagnetism

$$ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) $$

$$ \nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} $$

Quantum Mechanics

$$ \hat{p} = -i\hbar\frac{\partial}{\partial x} $$

$$ \Delta x \cdot \Delta p \geq \frac{\hbar}{2} $$

Statistics

$$ \bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i $$

$$ \sigma^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2 $$

$$ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} $$

Machine Learning

$$ J(\theta) = -\frac{1}{m}\sum_{i=1}^{m}[y^{(i)}\log(h_\theta(x^{(i)})) + (1-y^{(i)})\log(1-h_\theta(x^{(i)}))] $$

$$ \text{softmax}(z_i) = \frac{e^{z_i}}{\sum_{j=1}^{K} e^{z_j}} $$

$$ \nabla_\theta J(\theta) = \frac{1}{m} X^T (h_\theta(X) - y) $$

Best Practices

1. Keep Formulas Readable

❌ Too dense

$\frac{\frac{a}{b}+\frac{c}{d}}{\frac{e}{f}-\frac{g}{h}}$

✓ Broken into steps

Let $x = \frac{a}{b} + \frac{c}{d}$ and $y = \frac{e}{f} - \frac{g}{h}$

Then the result is $\frac{x}{y}$

2. Use Display Mode for Complex Formulas

❌ Complex inline

The integral $\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$ is fundamental.

✓ Display mode

The Gaussian integral: $$\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$$

3. Add Context

Theorem: For any triangle with sides $a$, $b$, $c$:

$$a^2 + b^2 = c^2$$

where $c$ is the hypotenuse.

4. Use Aligned for Multi-Step

$$ \begin{aligned} \text{Given: } & x + y = 5 \ \text{And: } & x - y = 1 \ \text{Adding: } & 2x = 6 \ \text{Therefore: } & x = 3, y = 2 \end{aligned} $$

Common Mistakes

❌ Missing escape for special characters

$50%$ (error!)

✓ Escaped correctly

$50%$

❌ Missing braces for multi-character

$x^10$ (shows x¹0)

✓ With braces

$x^{10}$

Output Format

When creating math content:

[Topic Title]

[Brief explanation of the concept]

Definition/Formula: $$ [Main formula in display mode] $$

Where:

• $[variable]$ = [meaning]
• $[variable]$ = [meaning]

Example: [Step-by-step solution]

$$ \begin{aligned} \text{Step 1: } & [equation] \ \text{Step 2: } & [equation] \ \text{Result: } & [final answer] \end{aligned} $$