physics
Biot-Savart Law
$$B(r) = \frac{\mu_0}{4\pi} \int \frac{I d\ell \times r'}{|r'|^3}$$
Canonical Partition Function
$$Z = \sum_{i} e^{-\beta E_i}$$
Grand Canonical Partition Function
$$\Xi = \sum_{i} e^{\beta ( \mu N_i - E_i)}$$
Hydraulic Diameter
$$D_h = \frac{4A_c}{P}$$
Reynolds Number
$$Re = \frac{\rho v L}{\mu}$$
Kinematic Viscosity
$$
u = \frac{\mu}{\rho}$$
Snell's Law
$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$
Bernoulli's Principle
$$P + \frac{1}{2} \rho v^2 + \rho g h = \text{const}$$
Hydrostatic Equation
$$\frac{dP}{dz} = - \rho g$$
Specific Gravity
$$SG = \frac{\rho}{\rho_{H_2O}}$$
Specific Weight
$$\gamma = \rho g$$
Viscosity
$$\tau = \mu \frac{\partial u}{\partial y}$$
Coulomb's Law
$$F = \frac{k q_1 q_2}{r^2}$$
Relativistic Addition of Velocities
$$u = \frac{v + u'}{1 + \frac{v \cdot u'}{c^2}}$$
Maxwell's Equations
$$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0},\ \nabla \cdot \mathbf{B} = 0,...$$
Newton's Law of Cooling
$$\frac{dT}{dt} = -k(T - T_{\text{env}})$$
Boltzmann Entropy
$$S=k_B\ln\Omega$$
Modulus of Resilience
$$U_r = \int_{0}^{\epsilon_Y}\sigma\mathop{d\epsilon} \approx \frac{\sigma_{YS}^2}{2E}$$
Modulus of Rigidity/Shear Modulus
$$G = \frac{\tau}{\gamma}$$
Modulus of Toughness
$$U_t = \int_{0}^{\epsilon_f}\sigma\mathop{d\epsilon}$$
Poisson's Ratio
$$\nu = - \frac{\epsilon_x}{\epsilon_z} = -\frac{\epsilon_y}{\epsilon_z}$$
Resistance in a straight conductor
$$R = \frac{\rho l}{A}$$
Thermal expansion
$$\Delta L = L_0 \alpha \Delta T$$
Light Wavelength and Frequency Relationship
$$c = \lambda f$$
Photon Energy
$$E = hf$$
Schrodinger's Equation
$$\scriptsize i\hbar\frac{\partial}{\partial t}\Psi(x,t) = \left[-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V(x,t)\right]\Psi(x,t)$$
Lorentz Transformations
$$x' = \frac{x-vt}{\sqrt{1-v^2/c^2}}$$
Hooke's Law (Modulus of Elasticity)
$$\frac{F}{A} = E\frac{\Delta L}{L}$$
Hooke's Law (Spring Constant)
$$F = -kx$$
Ampere's Law
$$\oint \vec{B} \cdot d\vec{l} = \mu_0 I$$