Math 224-01: Differential Equations: Reading Homework 5.2
- Properties of Systems :
- Terminology : what is the normal form of an IVP for a first-order differential system? what do we mean by ``n-vectors''? what are the state variables in the problem? are we generally able to solve systems?
- Point : what is the fundamental theorem for systems? how many conditions are there in this theorem? how many conclusions?
- Autonomous Systems, Equilibrium Points, Cycles : what is an autonomous IVP? what remarkable property is true of an autonomous system? how is x(t+c) related to x(t) anyway?
- Point : what is true about orbits of autonomous systems? (what's an orbit?)
- Point : what is an equilibrium point of an autonomous system?
- Point : what is a cycle?
- Planar Autonomous Systems, Direction Fields : what is a position vector for a planar autonomous system? how is the tangent to the orbit related to the differential equations?
- Point : what is a direction field for a planar autonomous system?
- Point : how are nullclines defined for a system? what do they tell us about orbits?
Math 224-01: Differential Equations: Reading Homework 5.2
Last Modified: Wed Mar 29 08:40:54 2000
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