Approximations and Rules of Thumb

Pi seconds are a nano-century.  ($\pi \approx 3600 * 24 * 365 * 100 * 10^{-9}$)

Maximum current on PCB trace: 500mA per 10mil 1oz trace.

PCB 1oz resistance: $0.5m\Omega/\Box$

RC: 1 RC ~ 0.63, 3 RC ~ 0.95, 7 RC ~ 1 - 0.1%

Parallel resistance:  $R_1 || R_2 \approx R_1 (1 - \frac{R_1}{R_2})$,  $R_1 \ll R_2 $

Quadratic equation:  $s^2 + 2\zeta s + 1 = 0$

                                   $s = -2\zeta, -1/2\zeta$,  $\zeta \gg 1$  

Tolerance: $(1+\alpha)(1+\beta) \approx  1 + \alpha + \beta$,   $\alpha,\beta \ll 1$

                $(1+\alpha)/(1+\beta) \approx  1 + \alpha - \beta$

                $\sqrt{1+\alpha} \approx 1+\alpha/2$  

                $(1+\alpha)^k \approx 1+k \alpha$