implicit_function_theorem.pdf
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Math230a (Fall 2025) Yum-Tong Siu 1 Implicit Function Theorem In our discussion of the proof of Stokes’s theorem for the case of a bounded domain D in R2 with piecewise continuously differentiable boundary, we put off the question the relation between a piece of the boundary defined by a continuously differentiable function with nonzero gradient and a curve parametrized by a continuously differentiable function. An answer to the question necessitates the introduction of the implicit function theorem which we now do.…
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