ABSTRACT
Mathematics has been considered the language of nature since the days of Galileo and in modern times it is considered the mother of all technologies. Differential equations were invented in the course of investigations of the laws that govern the physical world. Modern methods for solving differential equations and their practical applications constitute major portions of mathematics curricula for engineering and science students. Leibnitz invented some of the methods but the general theory for differential equations was developed by an electrical engineer, Augustin-Louis Cauchy. This chapter presents basic methods for solving ordinary differential equations and developing modeling techniques for application to real world problems. It covers methods for dealing with separation of variables, undetermined coefficients, parameter variations, Cauchy-Euler and Laplace transform methods, and series solutions are some of the classical methods. Mathematical formulations of laws containing derivatives are differential equations (DEs).
