Math 224-01: Differential Equations: Reading Homework 2.5

1. Approximate Solutions : what do we see in this section?
   
   1. Euler's Method : what idea characterizes Euler's method?
      
      1. Point : what are the ``partition'' and ``steps'' we use for Euler's method?
         
      2. Point : if we know that (t₀,y₀) is a point on a solution curve, how does Euler's method estimate (t₀+h,y₁)?
         
      3. Point : what is the ``Euler solution''?
         
   2. One-Step Methods : what is a one-step method?
      
   3. Error : what are the two types of error we consider in numerical methods?
      
      1. Point : what do we mean by the ``order'' of a one-step numerical method? what is the order of Euler's method?
         
   4. Other Methods : how is Heun's method different from Euler's method? how is Runge-Kutta different?