There is a deep relationship between the technique of separation of variables for solving partial differential equations and the symmetries of the underlying differential equations, as well as the special functions that often arise in this procedure. Advertisements
In this article I will apply the ideas from part 1 to the theory of rotations in three dimensions. (The theory of rotations in an arbitrary number of dimensions is similar, but for reasons of familiarity and simplicity I will … Continue reading
There is a deep relationship between being able to solve a differential equation and its symmetries. Much of the theory of second order linear differential equations is really the theory of infinite dimensional linear algebra. In particular Sturm-Liouville theory is … Continue reading
This is a follow up post to my previous post on . Mathematicians will often write without being clear of the context and structure associated with it.
In mathematics and physics it is common to talk about when really we mean something else that can be represented by . Consider mechanics or geometry, these are often represented as theories in , but really they don’t occur in … Continue reading