Everything about Implicit function theorem
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by can also be specified as the graph of a function, so that for each point on part of the curve,. An example is the unit circle, whose points satisfy, which can locally be solved by, expressing the top semicircle as a graph. It is not always possible to solve the equation for algebraically, and the implicit function theorem gives analytic conditions under which there exists a function whose graph belongs to the given curve, and, in some formulations, also gives a way of constructing approximations to. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Implicit function theoremA 5-minute orientation
- Skim a recent paper: Characterizing Smooth Safety Filters via the Implicit Function TheoremInfluential work since 2022
- Pick up a classic book: Fundamental existence theoremsThe most-reprinted book on the subject
- Read the landmark paper: An implicit function theoremCited 50 times
- Go sideways: Jacobian matrix and determinantA closely related topic
- Go sideways: Critical point (mathematics)A closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
An implicit function theorem
An implicit function theorem: Comment
Implicit function theorem over free groups
The implicit function theorem for ultradifferentiable mappings
Robinson’s implicit function theorem and its extensions
On the Nash-Moser implicit function theorem
IMPLICIT FUNCTION THEOREM IN CARNOT–CARATHÉODORY SPACES
The implicit function theorem in degenerate problems
🆕 Influential since 2022
Characterizing Smooth Safety Filters via the Implicit Function Theorem
An inverse mapping approach for process systems engineering using automatic differentiation and the implicit function theorem
Global implicit function theorems and the online expectation–maximisation algorithm
On an extension of a global implicit function theorem
Estimates of the size of the domain of the implicit function theorem: a mapping degree-based approach
📚 Books worth reading
- 📕Fundamental existence theoremsGilbert Ames Bliss · 1964
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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