Handout4    Mathematics 427K    Uhlenbeck  September 22, l998


   Lecture 8  9/22  Solution of extra credit problem on exam, Suggestions
           for projects, homogeneous second order equations with constant 
           coefficients (3.1), page 128, #5-14, 17, 19.

   Lecture 9  9/24  Complex Roots (3.4)  Page 150,# 1-12  Page 151 #17,18,29
           30,31.

   Lecture 10 9/29  General theory  linear equations (3.2),(4.1)
           finding a specific solution by undetermined coefficients (3.6).
           page 144 #1-5 page 206 #7-10 page 145 24,25 page 171 1-6,9,11,12,
           13,14.

   Lecture 10 10/1  Repeated Roots and resonances (3.5)  and review. Optional
           problems page 171, 10 page 159 8-12.


  Try doing these exercises to check if you understood the lecture! Number
  2 asks you to guess from your experience so far in the course.


  1.  Find the general solution to the equation

       y" +5y'  + 4 y = 0.   What is the specific solution with y(0) = 0,
                             and y'(0) = 5?


  2.  From what you have learned about first order equations, can you guess
      a good way to solve 


      y" +  5y'  + 4y  =  16   with  y(0) = 4?  and y'(0) = 0.
      What is the general  solution?

      What is a rest point or equilibrium solution for a second order
      equation?