The Fourier transform of a function \(f(t)\) is defined as:
\[\displaystyle \hat{f}(\omega) = \int_{-\infty}^{\infty} f(t)\, e^{-i\omega t}\, \mathrm{d}t\]
Maxwell's equations in differential form unify
\(\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}\) and
\(\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}\).
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