| Title | Summary |
|---|---|
| The Astounding Athletic Power of Quadcopters | Professor Raffaello D'Andrea (ETH-Zurich) explains that mathematical models
built from ordinary differential equations are used to design and control autonomous "athletic" quadcopters. A single quadcopter is modeled by a twelve-dimensional first-order system. The quadcopter balancing a stick is modeled by a sixteen-dimensional first-order system. These systems of ordinary differential equations have forcing terms that represent the forces applied by the (usually) four propellers, which the computers control. Larger first-order systems are required to model multiple moving objects. Control theory uses these models and feedback from the cameras to determine how to control the propellers to optimize certain objective functionals. Control theory using models with differential equations arise throughout engineering, not just robotics! |
| Khan Academy: Intro to Differential Equations | Khan Academy video introducing ordinary differential equations. It shows how to verify that something solves an ordinary differential equation. It does not cover classification of differential equations as in this Chapter. This video offers links to additional videos that will make more sense after we cover more material. |
| 3blue1brown: Overview of Differential Equations: Chapter 1 | The Youtube channel 3blue1brown video introducing differential equations. It gives an animated introduction to the subject that ranges beyond our course. It explains that most differential equations cannot be solved analytically. This is why graphical and numerical techniques play an important role in our course. |
| 3blue1brown: But what is a Partial Differential Equation? | The Youtube channel 3blue1brown video introducing partial differential equations. This course does not cover partial differential equations, but prepares you to study them. This video gives some insight into how partial differential equations arise and are studied. |