Differential Equations in Action: From Modeling to Theory

A differential equation is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of the function at a point. There are different types of differential equations including ordinary differential equations, linear differential equations, partial differential equations, homologous differential equations, and nonlinear differential equations. These equations can also be classified based on the order and coefficients of the derivatives, which may be either constants or functions of the independent variable. Differential equations are used to model real-world situations involving change. Such equations usually involve derivatives with respect to time. In most cases, a real-life problem involves the rate of change of a variable being proportional to some function of the variable. Such situations can be conveniently modeled using differential equations. This book provides a detailed analysis of the theory and modeling of differential equations. It is appropriate for students seeking detailed information in this area of mathematics as well as for experts.