Integration

Abstract

The significance of the concept of integration as one of the most fundamental processes of mathematical physics is no doubt familiar to the reader. In fact, it is no exaggeration to claim that modern mathematics and physics started with this concept. Generally speaking, physical laws are given in local form while their application to the real world requires a departure from locality. For instance, the universal law of gravity is given in terms of point particles, actual mathematical points, and the law, written in the language of mathematics, assumes that. In real physical situations, however, we never deal with a mathematical point. Usually, we approximate the objects under consideration as points, as in the case of the gravitational force between the Earth and the Sun. Whether such an approximation is good depends on the properties of the objects and the parameters of the law. In the example of gravity, on the sizes of the Earth and the Sun as compared to the distance between them. On the other hand, the precise motion of a satellite circling the Earth requires more than approximating the Earth as a point; all the bumps and grooves of the Earth’s surface will affect the satellite’s motion.