On October 14, 2012, Felix Baumgartner skydived from a heigh of 39 km (24 mi), reaching an estimated speed of 1,342 km/hr (834 mph). He descended in free-fall for 4 minutes and 20 seconds. You can watch the footage, which is impressive and scary all at once. At about 2:30 into the video, he starts getting out of his capsule. The camera shot at 3:00 is terrifying. He jumps at 3:34. He deploys his parachute at 7:55. He lands at 12:37. What does this have to do with differential equations? Falling objects are one of the most fundamental problems modeled with first order differential equations.
By the end of this lesson, you should be able to:
- Determine the order of a given differential equation.
- Check if a given function is a solution to a differential equation.
- Explain the difference between a general solution and a particular solution.
- Interpret a first order differential equation as a slope field.
- Solve first order differential equations via separation of variables (when it is possible).
- Determine whether a given first order linear differential equation is homogeneous or inhomogeneous.
- Solve linear first order differential equations via integrating factors (when it is possible).
- Read Polking, Boggess and Arnold, Sections 2.1 - 2.4.
- Watch pencasts (linked above).
- Check yourself before you wreck yourself.
- Participate in online community.
In class, we will:
- Conduct discussion, Q&A.
- Demonstrate DFIELD software for plotting direction fields.
- Work on this activity (key).
After class, please:
- Do these problems.