Math 224-01: Differential Equations: Reading Homework 2.3--4

1. The Sensitivity Problem : what design problem is considered in this section?
   
   1. Sensitivity : what do we mean by sensitivity in an IVP?
      
      1. parameters : how does the book suggest ``tricking'' a solver into graphing the solution to an IVP for a number of different parameter values? what observation does the book make about sensitivity after looking at the effect of parameter variation?
         
   2. Response in Linear ODEs : what conclusion can we draw about the output of a linear ODE in response to a bounded input function?
      
      1. variation in forcing : how is tolerance related to the solution of a standard linear IVP? what is the ``ideal'' IVP that we talk about in this context? the ``actual'' IVP? what are we trying to proscribe to guarantee a response between the bounding values?
         
   3. Linear ODEs and Sensitivity : what conclusion can we draw about the sensitivity of linear ODEs? what do we mean by continuity in the data?
      
2. Introduction to Bifurcations : what do we see happening in this section? what expectation do we have about this?
   
   1. Bifurcation Analysis : what is bifurcation analysis?
      
      1. steps : what are the steps in bifurcation analysis?
         
      2. scaling : why do we scale the variables in a problem? how do we do this?
         
      3. analysis : what do we determine about equilibrium solutions and the bifurcation parameter?
         
      4. bifurcation diagram : what is a bifurcation diagram? what variables appear on its axes?