Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what ...

First‑order differential equations, linear and separable equations, integrating factors, applications. Second‑order linear differential equations. Fundamental solutions, linear independence, Wronskian ...

Heun functions, which generalise the well‐known hypergeometric functions, are solutions to the Heun differential equation – a second‐order linear differential equation with four regular singular ...