Math 240 (J. Wu) Homework #10 Due Mo,April 5



Due to the Easter weekend next week, this assignment can be turned in on Monday April 5.

READINGS:
  In Kreyszig, 8.1-8.6, 8.8-8.9 
  To be covered next week: 8.10-8.11,9.1-9.3

CORE PROBLEMS:
  Do all core problems in 8.1-8.6, 8.8-8.9

ADDITIONAL PROBLEMS:

  1. Show that
    y=e A(t-t_0)[k1 ...kn]T+eAtint(e-Asg(s),s=t_0..t)
    is the solution of the initial value problem
    y'=Ay+g(t), y1(t_0)=k1,...,yn(t_0)=kn,
    where A is an n by n constant matrix.
  2. Solve the initial value problem:
    y'1=y1+y2+cos(t)
    y'2=y2+sin(t)
    
    y1(2)=6,y2(2)=8.
    
  3. No other additional problems this week, since there are a lot of core problems already. (Hand in your solutions of core problems.)
  4. MAPLE ASSIGNMENT:

    Do the following problems from Kreyszig:
    
    8.6 # 10
    8.9 # 15