Math 224-01: Differential Equations: Reading Homework 1.4

1. Modeling with Linear ODEs :
   
   1. Balance Laws and Compartment Models : what is the underlying principle that leads to this type of model? how does this lead to the balance law?
      
      1. example : explain how the pollutant accumulation model is developed
         
   2. Initial Data and Input : how does the solution of a first-order linear differential equation show response to initial data and input?
      
      1. example : explain how this is shown in the solution to the pollutant model
         
      2. step functions : what is a step function? how may it be used to model a step from a input of 4 to an input of 0 at t=3?
         
   3. Solution Formulas : what is the other way that a general solution to a driven linear ODE may be developed/written?