Category

Theorems in calculus

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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

method of differentiating composed functions

Green's theorem

line integral around a closed curve to a double integral over its enclosed region

integration by parts

theorem that relates the integral of a product of functions to the integral of their derivative and antiderivative

intermediate value theorem

formula for the derivative of a product

divergence theorem

generalization of the fundamental theorem in vector calculus

Stokes' theorem

theorem in vector calculus

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

formula for the derivative of a quotient

list of differentiation rules

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Pappus's centroid theorem

theorem that, for a solid of revolution of a planar figure, the surface area equals the figure’s perimeter times the distance the perimeter’s centroid travels, and the volume equals the figure’s area times the distance the figure’s centroid travels

Fermat's theorem

method to find local maxima and minima of differentiable functions on open sets

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

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

Fubini's theorem

Leibniz integral rule

differentiation under the integral sign formula

Helmholtz decomposition

general Leibniz rule

generalization of the product rule in calculus

Reynolds transport theorem

3D generalization of the Leibniz integral rule

monotone convergence theorem

theorem of calculus

Darboux's theorem

theorem in real analysis

gradient theorem

method of differentiating single term polynomials

inverse functions and differentiation

calculus identity

Cantor's intersection theorem

theorem that a decreasing nested sequences of nonempty closed compact sets has nonempty intersection

generalized Stokes' theorem

statement about integration of differential forms on manifolds

reciprocal rule

differentiation rule

Integral of inverse functions

mathematical formula

linearity of differentiation

calculus property