Help:Formulas

The quadratic formula\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

The Pythagorean theorem\[a^2 + b^2 = c^2\]

Einstein's famous equation of mass-energy equivalence\[E = mc^2\]

The Navier-Stokes equation for fluid dynamics\[\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u} \cdot \nabla) \mathbf{u} = -\frac{1}{\rho}\nabla p + \nu \nabla^2 \mathbf{u}\]

The Schrödinger equation for quantum mechanics\[i\hbar \frac{\partial \psi}{\partial t} = \hat{H} \psi\]

Maxwell's equations for electromagnetism\[\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{aligned}\]