AARMS summer course lectures
 Multiple scales:

Multiple scales applied to Rayleigh oscillator
 Maple code for Rayleygh oscillator: copy&paste the following into
Maple:
restart;
ode := diff(u(t),t,t)+u(t)=eps*(1diff(u(t),t)^2/3)*diff(u(t),t);
envelope := 2/sqrt(1+3*exp(t*eps));
eps := 0.1;
sol := dsolve({ode, u(0)=1, D(u)(0)=0}, numeric, maxfun=0);
with(plots):
odeplot(sol, [[t, u(t)], [t, envelope]], 0..100, numpoints=1000);
 Multiple scales applied to u''+u=eps*u^2
 Delay differential equations
 Homework 1  Partial solutions
 Using multiple scales to get a Complex Ginzburg Landau PDE from a PDE with a delay
 Rapidly convergent series for the
regular part of modified Green's function on a rectangle:
resummation.
 Homework 2. Due Thursday