Math 224-01: Differential Equations: Reading Homework 1.1

1. First-Order Differential Equations and Models :
   
   1. Differential Equations and Modeling : what characteristic of DEs appears in the first sentence of this section? in the fish population model, what terms are on the left- and right-hand sides of the equation?
      
      1. Point : what is a differential equation? what terms does it include?
         
      2. Point : what is a solution to a differential equation? what is an initial condition?
         
   2. Solutions : how does the book derive the solution to the simple no overcrowding fish model? what other solution does it obtain?
      
      1. Point : what is an equilibrium solution?
         
      2. Point : what is a solution curve? how is it different from a solution?
         
   3. Numerical Solutions : what can numerical solvers do? why are there many different curves in figures 1.1.n?