EquationsAdvanced formatting examples of real equations from math and physicsMass-Energy RelationE = mc2where m = Relativistic Massc = The speed of light in a vacuumLorentz Factor Definitionγ = 11 − v2c2where v = Velocityc = The speed of light in a vacuumRelativistic Mass Relationm = γm0where m = Relativistic Massm0 = Rest massγ = Lorentz factorObserver timet = γt − vxxc2where γ = Lorentz factort = Timevx = Velocity in the x directionx = x-coordinatec = The speed of light in a vacuumObserver xx = γ(x − vxt)where
γ = Lorentz factort = Timevx = Velocity in the x directionx = x-coordinateSchrodinger Equation in one dimensionitΨ(x, t) = 22m 2x2 + V(x, t)Ψ(x, t)where i = Imaginary Unitt = TimeΨ = Schrodinger wave function = Reduced Planck constantx = x-coordinateV = Potential energyCorrelation Testχ2 = (xi − x)(yi − y)ni = 1(xi − x)2ni = 1(yi − y)2ni = 1where i = Summation indexx = Independant variable xy = Independant variable yx = Average over all xy = Average over all ySpherical Electric FieldE ⋅ dA = 2πR2Ewhere E = Electric Field VectorA = Spherical surface tangent vectorR = Sphere radiusE = Electric chargeFalling in constant gravity with no air resistancey(t) = y00vy00g dtdt = vy0t + y0 − 12gt2where
t = Timet0 = Initial timey = y-coordinatevy0 = Velocity in the y directiony0 = Initail y positiong = Gravitation acceleration at the surface of the earth