Questions on "Partial Differential Equations", as opposed to "ordinary differential equations".

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General form of a connection with zero curvature

I am looking for proofs of the following two theorems: Theorem 1. On a connected and simply-connected open set $\Omega\subset\mathbb{R}^3$, functions $L^p_{ij}\in C^1(\Omega)$ are given that satisfy ...
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MATLAB, 1st order 2d hyperbolic equation, problem with convergence.

Follow up to my previous question: MATLAB: solving 1st order hyperbolic equation in 2 spacial dimensions The equation I'm solving has the form: $$f_t + A y f_x - B x f_y =0$$ I wrote the following ...