APPLICATIONS OF DIFFERENTIAL EQUATIONS, KPR Institute Engineering and Technology, Autonomous Engineering Institution, Coimbatore, India

In this Webinar, Applications of Differential equations are going to be explained in various fields like control theory, dynamical systems , circuit theory and so on. Basically the importance of mathematics in day to day life will also be explained. It will be briefly discussed how the students are applying the differential equations in their projects. In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

The study of differential equations consists mainly of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are soluble by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.