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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Implicit function theorem on curves

I am trying to figure out, whether the IFT can be generalized to curves. Let's say I have a function $G(x,u)$ mapping $\mathbb{R}^{n+m}\rightarrow \mathbb{R}^n$ with invertible jacobian $\frac{\partia …