Hi
How is it possible to solve a heat problem pde with boundaries which is not an straight line, but it is sinusoidal line?

I'm not sure how to decide which terms in first approximation in two-scale method are secular. I've studied the Problem Set 8 (equations after (6) and (8)). I don't understand why for example 2A*i*exp(i*t) is the secular term. Note that it will never increase as time goes to infinity and gives only oscillation behavior (its amplitude is time independent). The terms with exp(3*i*t) are similar, however they are not consider as secular terms. What is the reason for it? What secular terms exactly mean in this approach?