inż. Krzysztof Czuba

Test formatowania symboli

$$ \begin{aligned} \oint_{\partial \Sigma} \mathbf{E} \cdot d\boldsymbol{\ell} &= -\frac{d}{dt} \iint_{\Sigma} \mathbf{B} \cdot d\mathbf{S} \quad &\Longleftrightarrow \quad \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\[6pt] \oint_{\partial \Sigma} \mathbf{B} \cdot d\boldsymbol{\ell} &= \mu_0 \iint_{\Sigma} \left( \mathbf{J} + \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right) \cdot d\mathbf{S} \quad &\Longleftrightarrow \quad \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{aligned} $$

$$ \mathcal{F}\left\{ e^{-\pi \mathbf{x}^{\mathsf{T}} A \mathbf{x}} \right\}(\boldsymbol{\xi}) = \int_{\mathbb{R}^n} e^{-\pi \mathbf{x}^{\mathsf{T}} A \mathbf{x}} \, e^{-2\pi i \, \boldsymbol{\xi} \cdot \mathbf{x}} \, d^n\mathbf{x} = \frac{1}{\sqrt{\det A}} \exp\!\left( -\pi \, \boldsymbol{\xi}^{\mathsf{T}} A^{-1} \boldsymbol{\xi} \right), \qquad A = \begin{pmatrix} a_{11} & \cdots & a_{1n} \\ \vdots & \ddots & \vdots \\ a_{n1} & \cdots & a_{nn} \end{pmatrix} \succ 0 $$