Differential equations of the first order as mathematical models of reality

The article considers the applied value of the theory of differential equations of the first order, in particular, describes mathematical models for solving problems in chemistry, physics, ecology and the economic model of Evans establishing an equilibrium price; The importance of studying this topic by students of physical and mathematical specialties in higher educational institutions and students who are interested in the natural and mathematical sciences is shown.

Differential equations and their systems are quite important in the study of chemical processes. In their analysis in chemical systems, it is always assumed that every arbitrary process is carried out by a certain driving force. Thus, for diffusion, the driving force is the concentration gradient, convection is the density gradient, the heat flux is the temperature gradient, and so on. Therefore, objective analysis of these processes is possible only when applying differential equations, since the concept of gradient is closely related to the concept of a derivative.

Another area that uses the benefits of differential equation theory for its development and improvement is ecology. As the main object of her research, they consider the evolution of the population of living organisms. We describe differential population models that are associated with reproduction or extinction, as well as with the coexistence of different animal species in predator-prey cases.

But in addition to the natural sciences discussed above, this theory is quite widespread in other fields. For example, for an economy where no experimentation is possible, mathematical modeling is the most effective method for research through the use of a powerful mathematical apparatus. Examples of economic models are consumer choice models, economic growth models, equilibrium models in commodity, factor and financial markets and more.