Maxwell Equations Derived from (Coulomb’s Law + velocity), Maxwell-type Gravity Derived from (Newton Law + Velocity), Spin-Electromagnetism Derived from (Coulomb’ Law + Spin) --- by Universal Mathematical Field Theory (UMFT)

A Universal Mathematical Field Theory (UMFT) is established, which states that the combination of the operations of both gradient and divergence of vector fields, such as electric field and velocity field, create the curl of an axial vector field, such as magnetic field. Utilizing UMFT, we mathematically: (1) derive the Extended-Maxwell equations and the Lorentz force from Coulomb’s law and the velocity of the source; (2) establish Maxwell-type gravitational equations and Lorentz-type gravitational force (Gravito-EM) from Newton’s law and velocity of gravitational source; (3) establish Classical-Spin-Electromagnetism (Spin-EM) from the Coulomb’s law and the spin of the spin angular velocity; (4) predicate the Spin related force. For a source moving with non-spatially-varying velocity the Extended-Maxwell equations reduce to Maxwell equations, which justifies UMFT and shows that the experiments-based Maxwell equations have mathematical origin. This derivation mathematically explains how a moving electric charge creates magnetic field, and shows that there is no magnetic monopole charge. UMFT shows that mathematical identities lead to physical dualities including duality between EM and Gravito-EM. The concepts, effects and phenomena of EM may be directly converted to that of gravity. The Gravito-EM are employed to study the accelerating universe, rotation curve and gravitation waves. The Gravito-EM can be quantized, along the line of quantizing EM, and unified with EM force. We derive, for the first time, the Spin-Lorentz-type force and Lagrangian-Lorentz-type force. If experimentally proved, the Spin-related force may be the 5th force. UMFT provides mathematical origins of physical dualities between Extended EM, Gravito-EM and Spin-EM.