Calculus

Results named in Tau Ceti's TauCeti.Analysis.Calculus modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

Cartan's formula to The relative Poincaré lemma

• Cartan's formula
• Duhamel's formula at a small parameter
• Green's theorem on a rectangle
• The inverse function theorem produces a C^n inverse
• The inverse function theorem, with a C^n inverse on the whole target
• Iterated Rolle's theorem
• Jacobi's adjugate formula, valid at singular as well as invertible matrices
• Jacobi's inverse formula
• The Lefschetz–Whitehead rank estimate
• The local Morse lemma
• The Morse form of the convergence theorem
• The Morse form of Łojasiewicz's gradient inequality
• The Morse lemma
• Moser's identity
• Nijenhuis–Lie-derivative identity
• The parametric Morse lemma, as a local chart
• Peano's theorem on mixed partial derivatives, differentiating a time derivative in space
• The Poincaré lemma
• Rademacher's theorem for locally Lipschitz functions
• The relative Poincaré lemma

Rolle's theorem for finitely… to Uniform first-order Taylor…

• Rolle's theorem for finitely many zeros
• Sard's lemma on the flat stratum
• Sard's theorem on the locus where the derivative vanishes
• Stokes' formula on the boundary of a cube for a closed two-form ψ that is C¹ on (ℝ × ℝ) × ℝ
• Stokes' theorem on the standard simplex
• Taylor's formula to second order
• Taylor's theorem with a bounded remainder
• Uniform first-order Taylor estimate in a parameter

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