Math 224-01: Differential Equations: Reading Homework 1.2
- Visualizing Solution Curves : what motivation does the book give for using the differential equation to visualize its solution, rather than using a numerical solver? what is a solution to a differential equation?
- Solution curves : what knowledge allows us to use a numerical solver to find approximate solution curves?
- existence and uniqueness of solutions : what conditions guarantee the existence of a unique solution to an initial-value problem? what implication does this have any two solution curves to the IVP?
- geometry of solution curves : what is the geometry behind saying that y(t) is a solution of an ODE? how is a direction field related to this?
- Nullclines and equilibria :
- nullclines : what is a nullcline? how does a solution curve cross a nullcline? is a nullcline a solution curve?
- equlibrium solutions : what is an equilibrium solution to an ODE? how is one related to a nullcline? how would you find an equilibrium solution to an ODE?
- Compression and zooming : how is it that solution curves generated by a numerical solver can appear to touch?
Math 224-01: Differential Equations: Reading Homework 1.2
Last Modified: Thu Jan 21 21:19:46 1999
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