Math 224-01: Differential Equations: Reading Homework 2.3

1. Sensitivity : what does sensitivity mean? how is this related to controlling a system?
   
   1. Parameters : how are parameters related to the behavior of a system? how does the book suggest coaxing a numerical solver into analyzing the effect of changing a parameter in an ODE?
      
      1. Point : if the forcing q(t) is bounded, can a linear first-order IVP have a solution that blows up?
         
   2. Limits on Response : the book introduces the differential equations y'+p(t) y = q(t) and Z' + p(t) Z = m(t); what is the difference between the two? what deviation are we trying to estimate? what differential equation does it satisfy?
      
   3. A Fundamental Theorem : what is the conclusion of our sensitivity analysis for linear IVPs?
      
      1. Point : what is ``continuity in the data''?
         
      2. Point : what is a ``well posed'' IVP?