The Galilean-boost space-time transformation implies that accelerations are unchanged by changes of the relative constant velocity of the measuring instruments. Newton's Second Law then suggests that forces are also unchanged, but the torque a constant-velocity charge exerts on a compass needle at its point of closest approach changes with that velocity. This conflict motivates us to solve for the electromagnetic fields of a point charge moving at constant velocity, and to then inspect the results for the correct extension of the Galilean boost, a program we carry out by first deriving the electromagnetic wave equations, which we solve by Fourier methods, including indirectly via obtaining their causal Green's function. The constant-velocity point charge's electromagnetic fields display the space part of the Lorentz boost, which for infinite lightspeed becomes the space part of the Galilean boost. The time part of the Lorentz boost follows from its space part and the reciprocity of measuring instruments which have relative constant velocity. The frequently-presented consequences of the Lorentz boost are then developed in detail, as is the less familiar surprising Thomas-precession rotation produced by acceleration not parallel to velocity.