Math 224-01: Differential Equations: Reading Homework 3.4

1. Undriven Constant Coefficient Linear ODES, II : what do we do in this section? what is true about characteristic roots for an ODE with oscillatory solutions?
   
   1. Complex-Valued Functions : how is a complex-valued function written? what is its complex conjugate? how does the differentiation operator work on complex-valued functions?
      
      1. complex exponentials : what is Euler's formula? what are the real and imaginary parts of a complex exponential?
         
   2. Solution Formulas : what is the real-valued solution formula for a linear constant coefficient ODE having a characteristic equation with complex roots?
      
      1. justification : under what circumstances is a complex function y(t) real-valued? what is the general complex-valued solution to a second-order ODE? what steps lead us from this to the general real-valued solution?