Introduction
Ordinary differential equations are a powerful and essential tool in both theoretical and applied mathematics. Their ability to model dynamic systems, whether simple or complex, makes them indispensable in understanding the behavior of many real-world systems.
Learning objectives
After this part, you should be able to formulate an initial value problem, identify the assumptions that ensure a meaningful solution, and select and analyse a one-step numerical method in terms of order and stability.
With advanced techniques and numerical methods, ODEs continue to play a crucial role in scientific research, engineering design, and beyond. Understanding ODEs is therefore central to many fields of study, from physics and engineering to biology and economics.