Differential equations, studying the unsolvable: Differential Equations - Part 1 of 5

The video explores differential equations, highlighting their importance in physics and beyond. It distinguishes between ordinary and partial differential equations, providing examples and solving simple cases using integration. The complexity of higher-order equations is discussed, with a focus on the pendulum as a case study. The concept of phase space is introduced, and the video concludes with numerical solutions and chaos theory, emphasizing the challenges in predicting complex systems.

How does air resistance affect the motion of a pendulum according to the differential equation?

What is phase space and how is it relevant to the study of differential equations?

Discuss the concept of stability in the context of differential equations using the pendulum as an example.

How can numerical methods be used to approximate solutions to differential equations?