Everything about Inverse function theorem
Theorem in mathematics
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that if the best linear approximation to the function at a point is invertible, then with sufficient regularity assumptions, the function should also be invertible near that point. In its simplest form, the theorem states that if a real function f is differentiable in an open interval, with a continuous derivative, then in a neighborhood of any point where the derivative is not zero, f has an inverse function. The inverse function is also continuously differentiable, and the inverse function rule expresses its derivative as the multiplicative inverse of the derivative of f. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Inverse function theoremA 5-minute orientation
- Skim a recent paper: An inverse mapping approach for process systems engineering using automatic differentiation and the implicit function theoremInfluential work since 2022
- Pick up a classic book: Invitation to classical analysisThe most-reprinted book on the subject
- Read the landmark paper: The inverse function theorem of Nash and MoserCited 733 times
- Go sideways: Implicit function theoremA closely related topic
- Go sideways: Differentiable functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
The inverse function theorem of Nash and Moser
On the inverse function theorem
Convergence of Newton’s method and inverse function theorem in Banach space
Global inverse function theorem
Periodically perturbed conservative systems and a global inverse function theorem
An inverse function theorem for free groups
An inverse function theorem in Fréchet spaces
An inverse function theorem in Fréchet-Spaces
🆕 Influential since 2022
An inverse mapping approach for process systems engineering using automatic differentiation and the implicit function theorem
Inverse function theorem on the class of holomorphic self-maps of a disc with two fixed points
Hadamard inverse function theorem proved by variational analysis
The inverse function theorem for curved $L$-infinity spaces
Unconventional free fall measurements of g: involving the Pythagorean Theorem and inverse tangent function
📚 Books worth reading
- 📕Invitation to classical analysisPeter L. Duren · 2012
Spectral analysis, differential equations, and mathematical physicsFritz Gesztesy, H. Holden · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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