Modeling Using Differential Equations
The main use of first order differential equations is in modeling how different aspects of our world change over time. This class will be spent as a problem solving session to try to get used to modeling. In particular, we will try to solve the following two problems:
A Leaky Container
For a cylindrical can of radius
Rocket Motion
In straight-line motion, we can use Newton's second law to write the acceleration of an object as the sum of the forces on the object. However, if the mass of the object is changing over time, then we can rephrase Newton's second law to be in terms of a change in an object's momentum. Thus
Suppose a rocket has mass