Category
page 1Theorems in real analysis
fundamental theorem of calculus
calculus theorem describing the duality of differentiation and integration
mean value theorem
on the existence of a tangent to an arc parallel to the line through its endpoints
L'Hôpital's rule
rule that uses derivatives to help evaluate limits involving indeterminate forms
Rolle's theorem
on stationary points between two equal values of a real differentiable function
intermediate value theorem
theorem
Taylor's theorem
approximation of a function by a truncated power series
extreme value theorem
theorem that states that the image of real function having real closed interval as domain, has maximum and minimum
Abel's theorem
theorem
Heine–Borel theorem
theorem about compact sets in Euclidean space
Fermat's theorem
method to find local maxima and minima of differentiable functions on open sets
inverse function theorem
theorem that, if a function is continuously differentiable with nonzero Jacobian determinant at a given point, then it is locally invertible near that point
implicit function theorem
theorem that, under a mild condition on the partial derivatives, the set of zeros of a system of equations is locally the graph of a function
dominated convergence theorem
theorem that, for a sequence of functions bounded in absolute value by an integrable function, then almost everywhere pointwise convergence implies L¹ convergence
Arzelà–Ascoli theorem
theorem
Dini's theorem
theorem
monotone convergence theorem
theorem of calculus
Riemann series theorem
theorem
Lusin's theorem
theorem
Darboux's theorem
theorem in real analysis
Hardy's inequality
inequality relating a real number greater than 1 and a sequence of non-negative numbers
Sturm's theorem
Count of the roots of a polynomial in an interval, without computing them
identity theorem
theorem that an analytic function is completely determined by its values on a countable subset that contains a converging sequence together with its limit
Lagrange inversion theorem
theorem
Nested intervals
Sequence in mathematics
Lebesgue differentiation theorem
in real analysis, the theorem that, for almost every point, the value of an integrable function is the limiting average taken around the point
Riesz–Fischer theorem
theorem
Kirszbraun theorem
mathematical theorem related to real and functional analysis
Caristi fixed-point theorem
theorem
Steinhaus theorem
mathematical theorem in real analysis
Fubini's theorem on differentiation
Śleszyński–Pringsheim theorem
mathematical theorem related to fractions
Routh–Hurwitz theorem
mathematical theorem