Differential Equations

In this chapter, the focus is on differential equations, which are equations involving unknown functions and their derivatives. These equations allow us to understand the relationship between these unknown functions and how they change over time or in response to different variables. Differential equations have widespread applications in fields such as physics, engineering, economics, and biology, as they provide a mathematical framework for modeling various phenomena. The chapter explores the main methods for solving differential equations using numerical techniques. While some differential equations can be solved analytically with explicit formulas, many real-world problems require numerical methods for obtaining solutions. Numerical methods involve approximating the solution by dividing the problem into smaller steps and computing the values of the unknown function(s) at each step. This approach allows us to tackle complex problems that may not have a straightforward analytical solution. To illustrate these numerical techniques, the chapter includes several MATLAB codes. The codes demonstrate how to apply these techniques to solve differential equations in different scenarios. By working through the examples, readers can gain a practical understanding of how to implement and use numerical methods to solve differential equations using MATLAB.