Mathematical Formulas in Zolt

Zolt integrates KaTeX for high-performance mathematical rendering. You can use LaTeX syntax for both inline and block formulas.

Inline Math

Use single dollar signs $ for inline formulas:

Block Math

Use double dollar signs $$ for standalone block formulas:

∫−∞∞e−x2dx=π\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}

Complex equations with alignment (using standard LaTeX environments):

(a+b)2=(a+b)(a+b)=a2+ab+ba+b2=a2+2ab+b2\begin{aligned} (a+b)^2 &= (a+b)(a+b) \\ &= a^2 + ab + ba + b^2 \\ &= a^2 + 2ab + b^2 \end{aligned}

Formulas with Attributes

You can apply Zolt attributes to formulas, such as IDs for referencing or custom styling:

∑i=1ni=n(n+1)2\sum_{i=1}^{n} i = \frac{n(n+1)}{2}

Practical Examples

Statistics

The standard normal distribution probability density function:

f(x)=1σ2πe−12(x−μσ)2f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}

Physics

Maxwell's Equations:

∇⋅E=ρε0\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}
∇⋅B=0\nabla \cdot \mathbf{B} = 0
∇×E=−∂B∂t\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}
∇×B=μ0(J+ε0∂E∂t)\nabla \times \mathbf{B} = \mu_0\left(\mathbf{J} + \varepsilon_0\frac{\partial \mathbf{E}}{\partial t}\right)

Trigonometry

FunctionIdentity
Sinesin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1
Tangenttan⁡θ=sin⁡θcos⁡θ\tan\theta = \frac{\sin\theta}{\cos\theta}

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