Glance at this Wikipedia article discussing the history and importance of rockets for defense, scientific research, space exploration, rescue, sport, and more. Differential equations -- and in particular, the basic understanding of the relationship between position, velocity, and acceleration -- have been, and continue to be, instrumental in the design of rockets.
By the end of this lesson, you should be able to:
- Distinguish between algebraic equations and differential equations.
- Determine the in/dependent variables in a differential equation.
- Give examples of phenomena modeled by differential equations.
- Translate verbal descriptions of change into differential equations, and vice versa.
- Solve directly integrable initial value problems.
- Explain and use the relationship between position, velocity, and acceleration.
- Read Polking, Boggess and Arnold, Chapter 1.
- Watch pencasts (linked above).
- Check yourself before you wreck yourself.
- Do some examples of integration by partial fractions, parts, and u-substitution.
- Work on this activity (key).
- Do post-class problems.