Mechanical engineering is an engineering branch that combines engineering physics and mathematics principles with materials science to design, analyze, manufacture, and maintain mechanical systems. It is one of the oldest and broadest of the engineering branches. Engineering Mechanics Rigid-body Mechanics • a basic requirement for the study of the mechanics of deformable bodies and the mechanics of fluids (advanced courses). • essential for the design and analysis of many types of structural members, mechanical components, electrical devices, etc, encountered in engineering.