Surface of revolution never negative, the area is given by If the curve is described by the function , , then the integral becomes for revolution around the -axis, and for revolution around the "y"-axis (using ). These come from the above formula. For example, the spherical surface with unit radius is generated by the curve , , when ranges over . Its area is therefore For the case of the spherical curve with radius , rotated about the -axis A minimal surface of revolution is the surface of revolution of the curve between two given points which minimizes surface area. A basic
Surface engineering Surface engineering Surface engineering is the sub-discipline of materials science which deals with the surface of solid matter. It has applications to chemistry, mechanical engineering, and electrical engineering (particularly in relation to semiconductor manufacturing). Solids are composed of a bulk material covered by a surface. The surface which bounds the bulk material is called the Surface phase. It acts as an interface to the surrounding environment. The bulk material in a solid is called the Bulk phase. The surface phase of a solid interacts with the surrounding environment. This interaction can degrade the surface phase over time. Environmental degradation of