physics

$$\small {d \over d t}A_H = \frac{1}{i\hbar}[A_H, H] + \left(\frac{\partial A_H}{\partial t}\right)$$

$$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0$$

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$

$$J = \Delta p = F \Delta t$$

$$T_p = 2 \pi \sqrt{\frac{\ell}{g}}$$

$$T_s = 2 \pi \sqrt{\frac{m}{k}}$$

$$B(r) = \frac{\mu_0}{4\pi} \int \frac{I d\ell \times r'}{|r'|^3}$$

$$Z = \sum_{i} e^{-\beta E_i}$$

$$\Xi = \sum_{i} e^{\beta ( \mu N_i - E_i)}$$

$$D_h = \frac{4A_c}{P}$$

$$Re = \frac{\rho v L}{\mu}$$

$$ u = \frac{\mu}{\rho}$$

$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$

$$P + \frac{1}{2} \rho v^2 + \rho g h = \text{const}$$

$$\frac{dP}{dz} = - \rho g$$

$$SG = \frac{\rho}{\rho_{H_2O}}$$

$$\gamma = \rho g$$

$$\tau = \mu \frac{\partial u}{\partial y}$$

$$F = \frac{k q_1 q_2}{r^2}$$

$$u = \frac{v + u'}{1 + \frac{v \cdot u'}{c^2}}$$

$$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0},\ \nabla \cdot \mathbf{B} = 0,...$$

$$\frac{dT}{dt} = -k(T - T_{\text{env}})$$

$$S=k_B\ln\Omega$$

$$U_r = \int_{0}^{\epsilon_Y}\sigma\mathop{d\epsilon} \approx \frac{\sigma_{YS}^2}{2E}$$

$$G = \frac{\tau}{\gamma}$$

$$U_t = \int_{0}^{\epsilon_f}\sigma\mathop{d\epsilon}$$

$$\nu = - \frac{\epsilon_x}{\epsilon_z} = -\frac{\epsilon_y}{\epsilon_z}$$

$$R = \frac{\rho l}{A}$$

$$\Delta L = L_0 \alpha \Delta T$$

$$c = \lambda f$$