## Archive of posts on Nov 6, 2022

• ### Solving linear homogeneous ODE with constant coefficients

By using power series, we can prove that the problem of solving linear homogeneous ODE with constant coefficients can be reduced to the problem of solving a polynomial with those coefficients. This article illustrates this point in detail, but it uses a very awful notation…

• ### Thoughts on a middle school thermal physics problem

To heat an object with hot water, if we divide the water into more parts and use each part to heat the object one after another, the final temperature will be higher. If the number of parts tends to infinity, then the final temperature will tend to the limit $T+\mathrm e^{-\frac C{C_0}}\left(T_0-T\right)$, where $T$ is the initial temperature of the object, $T_0$ is the temperature of the hot water, $C$ is the heat capacity of the object, and $C_0$ is the heat capacity of the hot water.