Special Relativity
The Lorentz transformation is derived in the case of a general boost, where a vector of arbitrary direction represents the relative velocity of the two systems. The mathematics for the general case is derived from the same basic, elegant principle of the original article of Einstein
The relativistic formula for the composition of velocities, accelerations, and the transformation of forces is derived in this section from the general Lorentz transformation for a boost of arbitrary direction
In this section, we will derive the formula for the transformation of the Maxwell equations for a general boost in an arbitrary direction. In the literature, the derivation of the relativistic Maxwell equations is computed using differential geometry. Instead, Einstein used standard multivariate calculus in his original article, but in the easier case where the boost is along with one of the axes. The derivation using multivariate calculus of the relativistic Maxwell equations is much more challenging when the velocity has an arbitrary direction, and it is not generally found in the literature or on the web.