The Sturm_Liouville Boundary Value Problems and their applications: First Edition

The sturm_Liouville Boundary value problems, after the Swiss mathematician Jacques Sturm (1803¿1855) and the French mathematician Joseph Liouville (1809¿1882), who studied these problems and the properties of their solutions, is the most important branch of applied mathematics which form the starting point for the study of mechanical and electrical vibrations of all kinds of important phenomena. They give a method for solving many problems in science, and engineering such as heat flow in uniform and non-uniform rod, vibrations of a vibrating string, circularly symmetric heat flow, current flow in an electric circuit, and in quantum physics. The differential equations considered here arise directly as mathematical models of motion according to Newton¿s law, but more often as a result of using the method of separation of variables to solve the classical partial differential equations of physics, such as Laplace¿s equation, the heat equation, and the wave equation.