Could anyone give an intuitive idea of the meaning of differentiability in general in any dimension and any space?
2026-05-04 08:51:23.1777884683
Meaning of differentiability
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A differential map is a map than can be well approched by a linear map in a neighborhood of all points. The basic theorems in differential calculus (local form of immersions/submersions, implicit functions, local inversion) all give statements of the form: "we have a knowledge on the linear map that approaches the function (that is, its differential), then we have a local knowledge of the function itself".
Since linear algebra is much more simpler than analysis of functions, this explains why this idea is so important.