Integration

Abstract

It is not an exaggeration to say that the most important concept, whose mastery ensures a much greater understanding of all undergraduate physics, is the concept of integral. Generally speaking, physical laws are given in local form while their application to the real world requires a departure from locality. For instance, Coulomb’s law in electrostatics and the universal law of gravity are both given in terms of point particles. These are mathematical points and the laws assume 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.