Math 224-01: Differential Equations: Reading Homework 5.2

1. Properties of Systems :
   
   1. 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?
      
      1. Point : what is the fundamental theorem for systems? how many conditions are there in this theorem? how many conclusions?
         
   2. 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?
      
      1. Point : what is true about orbits of autonomous systems? (what's an orbit?)
         
      2. Point : what is an equilibrium point of an autonomous system?
         
      3. Point : what is a cycle?
         
   3. 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?
      
      1. Point : what is a direction field for a planar autonomous system?
         
      2. Point : how are nullclines defined for a system? what do they tell us about orbits?