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smooth function
Sign in to saveAlso known as infinitely differentiable function, smooth map
thumb|upright=1.2|A bump function is a smooth function with [[compact support.]]
~17 min read
Encyclopedic overview
22 sectionsContents
- Differentiability classes
- Examples
- Continuous (''C''<sup>0</sup>) but not differentiable
- Finitely-times differentiable (''C''<sup>{{mvar|k}}</sup>)
- Differentiable but not continuously differentiable (not ''C''<sup>1</sup>)
- Differentiable but not Lipschitz continuous
- Analytic (''C''<sup>{{mvar|ω}}</sup>)
- Smooth (''C''<sup>{{mvar|∞}}</sup>) but not analytic (''C''<sup>{{mvar|ω}}</sup>)
- Multivariate differentiability classes
- The space of ''C''<sup>''k''</sup> functions
- Continuity
- Parametric continuity
- Order of parametric continuity
- Geometric continuity
- Other concepts
- Relation to analyticity
- Smoothness and the Laplace transform
- Smooth partitions of unity
- Smooth functions on and between manifolds
- Smooth functions between subsets of manifolds
- See also
- References
{{redirect|C infinity|the extended complex plane \mathbb{C}_\infty|Riemann sphere}} {{redirect|C^n|\mathbb{C}^n|Complex coordinate space}}
thumb|upright=1.2|A bump function is a smooth function with [[compact support.]]
Excerpted from Wikipedia’s “smooth function” article, available under the CC BY-SA 4.0 licence.