Cristian Mesiano

In this post, we'll explore two pillars of multivariable calculus: The first is nothing but the extension in ℝ^n of the very well known Taylor series expansion. The second gives the entire numerical simulation world a simple test to check whether a numerical approximation is feasible or not: the Inverse Function Theorem.

Last time, we looked at Fréchet differentiability simply put, it's how we generalize the idea of a derivative in ℝ to multiple dimensions. In this post, the focus is on a crucial concept which has vast usage in both classical and quantum physics: conservative vector fields. The deep connection between conservative vector fields and potential functions hinges on Schwarz's Theorem. Partial/Total Differentiability It's worth to highlight that f(x_0 +h) = f(x_0)+l(h) + o(h) Geometrically, we are...

We have seen many times: despite being based on linear equations, the quantum world exhibits highly non-linear-looking phenomena.