https://doi.org/10.36719/2663-4619/110/93-97
Sabina Bashirova
State Administration Academy under the President of the Republic of Azerbaijan
https://orcid.org/0009-0001-1964-7221
bashirova.sabina310889@gmail.com
Differential Operators
Abstract
Differential operators are operators that calculate derivatives of functions and play an important role in mathematical analysis. It was created by Newton and Leibniz in the 17th century and widely applied in various fields of mathematics. These operators are used in linear and non-linear systems, wave, heat and diffusion equations. In mathematical models, differential operators of the first and second order are of special importance. Nowadays, digital solution methods, such as finite difference and finite element methods, are widely used to work with differential operators. Operator visualization and graphical analysis help better understanding of applications.
Future research will explore the application of these operators in new fields, especially in artificial intelligence.
Keywords: differential operator, mathematical equations, partial differential equations, linear operators, nonlinear systems, mathematical modeling, numerical methods, wave and heat equations