Math 224-01: Differential Equations: Reading Homework 2.3--4
- The Sensitivity Problem : what design problem is considered in this section?
- Sensitivity : what do we mean by sensitivity in an IVP?
- 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?
- Response in Linear ODEs : what conclusion can we draw about the output of a linear ODE in response to a bounded input function?
- 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?
- Linear ODEs and Sensitivity : what conclusion can we draw about the sensitivity of linear ODEs? what do we mean by continuity in the data?
- Introduction to Bifurcations : what do we see happening in this section? what expectation do we have about this?
- Bifurcation Analysis : what is bifurcation analysis?
- steps : what are the steps in bifurcation analysis?
- scaling : why do we scale the variables in a problem? how do we do this?
- analysis : what do we determine about equilibrium solutions and the bifurcation parameter?
- bifurcation diagram : what is a bifurcation diagram? what variables appear on its axes?
Math 224-01: Differential Equations: Reading Homework 2.3--4
Last Modified: Tue Feb 9 20:32:18 1999
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