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}
$$