Theory, Practice and Techniques in Differential Equations

Differential equations contribute a tremendously important and useful role in applied math, engineering, and physics, and much mathematical and numerical machinery has been developed for the solution of differential equations. A differential equation articulates a relationship between a function and its derivatives. Differential equations are at the heart of physics and much of chemistry. Differential equations have a remarkable ability to predict the world around us. They are used in a wide variety of disciplines, from biology, economics, physics, chemistry and engineering. They can describe exponential growth and decay, the population growth of species or the change in investment return over time. Over the last hundred years, many techniques have been developed for the solution of ordinary differential equations and partial differential equations. While quite a major portion of the techniques is only useful for academic purposes, there are some which are important in the solution of real problems arising from science and engineering. The importance of a differential equation as a technique for determining a function is that if we know the function and possibly some of its derivatives at a specific point, then this information, together with the differential equation, can be used to control the function over its entire sphere.

“Theory, Practice and Techniques in Differential Equations” covers the fundamentals of the theory and techniques of ordinary differential equations. It begins with an overview of differential equations with first order differentiate equation. Moreover, it illustrates the techniques of second order linear homogeneous differential equations. Primarily intended for the students of mathematics and physics, this text gives in-depth coverage of differential equations and the methods for solving them. In this work an attempt was made to assess the relative importance of various aspects of differential equations in the teaching of engineering students and to find out which types of equations were used in the various engineering disciplines.