Mathematical Modeling and Applications of Differential Equations in Science and Engineering

Analytically, differential equations are a means of developing relationships between functions that define rates of changes and these rates in terms of the underlying function. They are crucial in modeling diverse, evolutive systems within various domains, to list but a few: physics, engineering, biology, and economics. The fundamentals of differential equations are categorized mainly into Two types of Differential Equations are Ordinary Differential Equations and Partial Differential Equations. Most of the differential equations are solved analytically and numerically techniques such as separation of variables, Fourier series and finite difference techniques. In situations, where exact solutions are tough to come across, computational tools like MATLAB, Maple and the Python libraries help towards approximations. Because they help to explain how systems behave, as well as predicting and improving them, differential equations are an essential tool for expanding the body of scientific and engineering knowledge.