Recent content by StretchySurface

Suppose I'm solving $$y''(t) = x''(t)$$ where $$x(t)$$ is the ramp function. Then, by taking the Laplace transform of both sides, I need to know $x'(0)$ which is discontinuous. What is the appropriate technique to use here?

Ah okay, now I understand! Thank you very much!

Okay, so I don't really see the point you're trying to convey and how it relates to my question. Below, I'll write out a set steps in reasoning to see if you can pinpoint the error I'm making. Let's only consider the case ##n = 2## i.e traveling around the ring twice. Periodicity demands that...

Does that mean the following is untrue: We require ##U(s′,t)=U(s′+4πR,t)##?

I'm solving the heat equation on a ring of radius ##R##. The ring is parameterised by ##s##, the arc-length from the 3 o'clock position. Using separation of variables I have found the general solution to be: $$U(s,t) = S(s)T(t) = (A\cos(\lambda s)+B\sin(\lambda s))*\exp(-\lambda^2 kt)$$...