Principles of applied mathematics, James Keener.
Homwwork (all with respect to the new book), due Sept 13: 1.1:1,2,3,6,9a; 1.2:1,3,4;1.4:4
HW 1.3:2a,1.4:2,3,4 This handout All Due sept 20
HW:2.1:1,3,8,11; 2.2:2a,b,3,4,8b,9,14; Due Sep 27
Consider the equation:
Assume a(t) if periodic. Prove that either both Floquet multipliers are on the unit circle or that they are both real with one inside and one outside the unit circle. (Hint: write as a system and use the fundamental matrix).
Note that since I did not get to that much of 2.2, you can hand in the HW from section 2.2 next Friday instead of Wednesday
Suppose that f(0)=0 and f'(0) is nonzero. What is delta(f(x)) ?
Find parameters A,B,C such that there is more than one periodic solution to :
u'' + epsilon u' [ A + B u^2 + C u^4] + u = 0
All due Nov 20th
Use the method of averaging to find determine the range of the parameter b such that there are periodic solutions to this problem when eps is small:
y' = 1 + eps sin(y)(1-cos(x))^2 + eps b