Math 224-01: Differential Equations: Reading Homework 3.7

1. General Theory of Linear ODEs : what do we look at in this section? are we likely to be able to find solutions to it?
   
   1. Continuity Set : what is a continuity set a set of? what is C³([1,5])?
      
      1. Point : what is the fundamental theorem for a linear ODE?
         
      2. Point : what does the vanishing data theorem tell us?
         
   2. Operator Formulation : what are the domain and codomain of an operator?
      
      1. Point : we can think of an operator as a function. what are the input and output of a second order linear operator?
         
      2. Point : do the linearity and superposition principles apply to non-constant coefficient linear operators? why?
         
      3. Point : what is the null space of an operator?
         
      4. Point : what is the Wronskian of two functions?
         
      5. Point : what is a basic solution set for a second order linear equation?
         
      6. Point : how are basic solution sets and nullspaces related?
         
   3. All of those solutions : how can all solutions of a second order linear operator be expressed? Is it always possible to find a particular solution in this case?