# Recent content by JPaquim

1. ### Adding a total derivative to the Lagrangian

I'm sorry, but I'm just not finding it trivial. Could you write it out for me, please?

13. ### Figuring symmetries of a differential operator from its eigenfunctions

So, I understand that the derivative operator, D=\frac{d}{dx} has translational invariance, that is: x \rightarrow x - x_0, and its eigenfunctions are e^{\lambda t}. Analogously, the theta operator \theta=x\frac{d}{dx} is invariant under scalings, that is x \rightarrow \alpha x, and its...
14. ### Representing a factorial through its pseudo Z transform

Ok, so I was playing around with some Z transforms. I'm sorry about the long derivation, but I'm a bit unsure of the mathematical rigor, and want to make sure every step is clear. I started with the recurrence relation defining the factorial: $$n!: u_{n+1}=(n+1)u_n=u_n+nu_n$$ $$u_0 = 1$$...
15. ### Creating intuition about Laplace & Fourier transforms

I had thought about how the fact that the norm of the basis elements isn't really defined since the integral doesn't converge, but didn't really reach any conclusion... How can you justify integrating over a finite interval? You mention the Hilbert basis won't guarantee pointwise convergence...