Math 224-01: Differential Equations: Reading Homework 1.5

1. Introduction to Modeling and Systems : what is modeling? what are the interrelated steps to using models to explain outcomes of an observable situation?
   
   1. Systems : what is a differential system? a linear differential system?
      
   2. Models :
      
      1. radioactive decay : what is the decay law? what differential equation does it lead to? how does radiocarbon dating work?
         
      2. Galilean vertical motion : what is the logic leading to the Galilean model of vertical motion? how does Newton modify it?
         
   3. Dynamical Systems : what are the state variables of a model?
      
   4. Modeling : what is the (close-to) last step in the modeling process?
      
   5. IVPs : how are initial value problems related to modeling? how many initial conditions might we expect an IVP to have?