Partial differential equations

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   Let $u(x,t) = e^{-45\,t}\,\sin(3x)$. Compute the diffusivity $\alpha$ for which $u$ solves the heat equation $u_t = \alpha\,u_{xx}$.

2. Warm-up

   Let $u(x,t) = e^{-175\,t}\,\sin(5x)$. Compute the diffusivity $\alpha$ for which $u$ solves the heat equation $u_t = \alpha\,u_{xx}$.

3. Warm-up

   Let $u(x,t) = e^{-12\,t}\,\sin(2x)$. Compute the diffusivity $\alpha$ for which $u$ solves the heat equation $u_t = \alpha\,u_{xx}$.

Problems shown under their original terms: Generated (template, solver-computed).