Math 224-01: Differential Equations: Reading Homework 1.2

1. Visualizing Solution Curves : what motivation does the book give for using the differential equation to visualize its solution, rather than using a numerical solver? what is normal form? what is a solution to an ODE?
   
   1. Solution Curves : what odd observation is made about the existence of solution formulas for ODEs?
      
      1. Point : what circumstances guarantee a unique solution to an IVP? what is the implication of this?
         
   2. Geometry of Solution Curves : what is the geometric view of y(t) being a solution to y'(t) = f(t,y)? how do we draw a direction field?
      
      1. Point : what is a direction field? how does it show solutions?
         
      2. Point : what are nullclines? are they solution curves?
         
      3. Point : how are nullclines and equilibrium solution curves related? how are equilibrium solutions found?
         
   3. Compression and Zooming : why is it sometimes hard to find a solution curve passing through a specific point? how can we get around this? why can't the solution curves in this example touch?