Math 224-01: Differential Equations: Reading Homework 2.1

1. Existence and Uniqueness : why are initial value problems important?
   
   1. Basic Questions : what basic questions is this chapter concerned with? will we find answers?
      
   2. Existence and Uniqueness : when will an IVP be guaranteed a unique solution? over what region is this guaranteed?
      
      1. solution curves : what significant consequence does the existence and uniqueness theorem have? why?
         
   3. Exceptional Cases : what happens when the conditions of the existence and uniqueness theorem are not satisfied?
      
      1. piecewise continuity : how does jump discontinuity affect the existence or uniqueness of solutions to an ODE? to what IVPs is it applicable? is this different than the existence and uniqueness theorem?