Category
page 1Theorems in mathematical analysis
chain rule
method of differentiating composed functions
Stirling's approximation
approximation for factorials
integration by parts
theorem that relates the integral of a product of functions to the integral of their derivative and antiderivative
product rule
formula for the derivative of a product
Jensen's inequality
theorem of convex functions
quotient rule
formula for the derivative of a quotient
implicit function
function defined by a relation of the form 𝑅(𝑥,𝑦)=0, where 𝑅 is a function of several variables and there is a unique 𝑦 that satisfies the relation for every 𝑥
list of differentiation rules
Wikimedia list article
Gaussian integral
theorem
Euler–Maclaurin formula
theorem
Picard–Lindelöf theorem
theorem on existence and uniqueness of solutions to first-order equations with given initial conditions
Heine–Cantor theorem
theorem
Stone–Weierstrass theorem
theorem that every continuous function on a compact Hausdorff space can be approximated by certain families of continuous functions
Helmholtz decomposition
theorem
Pontryagin duality
duality for locally compact abelian groups
general Leibniz rule
generalization of the product rule in calculus
symmetry of second derivatives
theorem
power rule
method of differentiating single term polynomials
inverse functions and differentiation
calculus identity
Riemann–Lebesgue lemma
lemma that the Fourier transform of an L¹ function vanishes at infinity
Cauchy formula for repeated integration
theorem
Peano existence theorem
theorem
Poincaré inequality
Mathematical inequality in Sobolev space theory
universal approximation theorem
theorem that a feed-forward network with a single hidden layer can approximate continuous functions
Sard's theorem
theorem that the set of the critical values of a smooth function has measure zero
Hartman–Grobman theorem
theorem
Cauchy–Kowalevski theorem
local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems
Faà di Bruno's formula
theorem
Goldbach–Euler theorem
theorem stating that sum of 1/(k−1), where k ranges over positive integers of the form mⁿ for m≥2 and n≥2, equals 1
Hausdorff paradox
paradox in mathematics
Dirichlet conditions
theorem
Lax equivalence theorem
theorem that asserts that a consistent and stable numerical method is convergent
envelope theorem
theorem in mathematics and economics
Besicovitch covering theorem
theorem
reciprocal rule
differentiation rule
Poisson summation formula
an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform
Hölder's theorem
result on gamma function
Kantorovich inequality
Mathematical theorem
Lévy–Steinitz theorem
Agmon's inequality
Mathematical Equation
Markov brothers' inequality
inequality proved by Andrey Markov and Vladimir Markov
Fenchel–Moreau theorem
mathematical theorem in convex analysis
Wirtinger's inequality for functions
theorem
Bipolar theorem
theorem in convex analysis
Denjoy–Luzin theorem
Kantorovich theorem
theorem about initial conditions that insure the convergence of Newton's method
initial value theorem
mathematical theorem using Laplace transform
Helly's selection theorem
On convergent subsequences of functions that are locally of bounded total variation
Rellich–Kondrachov theorem
compact embedding theorem concerning Sobolev spaces
Sturm–Picone comparison theorem
mathematical theorem which provides criteria for the oscillation and non-oscillation of solutions of certain linear differential equations in the real domain
linearity of differentiation
calculus property
Integral of inverse functions
mathematical formula
Carathéodory's existence theorem
generalization of Peano's existence theorem