Electrons and Protons

electron mass = 9.10938188 × 10^-31 kilograms

proton mass = 1.67262158 × 10^-27 kilograms
elementary charge = 1.60217646 × 10^-19 coulombs

Limit Definition of e

e = 2.718

lim(1+1/n)ⁿ = e
n > inf

NB: lim(1+2/n)ⁿ = e²
n > inf

Inverse Trigonometric Derivatives & Integrals

Derivatives
d/dx arcsin(x) = 1 / (1-x²)^1/2
d/dx arccos(x) = -1 / (1-x²)^1/2
d/dx arctan(x) = 1 / (1+x²)

Integrals
S dx/(a²-x²)^1/2 = arcsin (x/a) + C
S dx/a²+x² = (1/a) arctan (x/a) + C
S dx/x(x²-1)^1/2 = arcsec (x) + C

List of Common Integrals

S = integral sign


S dx/(x²+a²)^3/2 = 1/a² * x/(x²+a²)^1/2
S x*dx/(x²+a²)^3/2 = -1/(x²+a²)^1/2

Kinematic Formulas

v_f = v_i + at
d = 1/2 (v_i + v_f)t
d = v_it + 1/2 a t²
v_f² = v_i² + 2ad