Math 224-01: Differential Equations: Reading Homework 2.5

1. Approximate Solutions : why might we be interested in obtaining numerical solutions to differential equations?
   
   1. Euler's method : what are the steps referred to in Euler's method? if h=.1 and t0=1, what is t3? how are the values y1, y2, etc., calculated?
      
      1. error in the Euler method : what is true about the error in Euler's method?
         
   2. One-Step methods : what is a one-step method? why is it called this? what is the ``approximate slope function'' for Euler's method?
      
      1. error : what is the global error of a numerical method? how is the accuracy of one-step methods characterized?
         
      2. Euler's method : what order (in terms of error) is Euler's method?
         
      3. Heun's method : what order is Heun's method?
         
      4. Runge-Kutta method : what order is the Runge-Kutta method?
         
   3. Systems : how can a numerical method be used to solve a system?