Math 224-01: Differential Equations: Reading Homework 1.1

1. First-Order Differential Equations and Models :
   
   1. Differential Equations : what is the key that leads differential equations to model things like populations?
      
      1. modeling with differential equations : how may birth and death rates for populations be modeled?
         
      2. ordinary differential equations : what is an ordinary differential equation? a solution to a differential equation? an initial condition? an initial value problem?
         
      3. solutions and solution curves : what is the difference between a solution to a differential equation and a solution curve?
         
   2. Numerical Solutions : how does the book obtain the graphs of the solution curves shown in figures 1.1.n? why are there many different curves?