Search results
Results From The WOW.Com Content Network
Cauchy's mean value theorem, also known as the extended mean value theorem, is a generalization of the mean value theorem. [ 6 ] [ 7 ] It states: if the functions f {\displaystyle f} and g {\displaystyle g} are both continuous on the closed interval [ a , b ] {\displaystyle [a,b]} and differentiable on the open interval ( a , b ) {\displaystyle ...
Mean value theorem; Inverse function theorem; ... This is also known as the nth root test or Cauchy's criterion. ... is the Basel problem and the series converges to ...
A Cauchy problem in mathematics asks for the solution of a partial differential equation that satisfies certain conditions that are given on a hypersurface in the domain. [1] A Cauchy problem can be an initial value problem or a boundary value problem (for this case see also Cauchy boundary condition). It is named after Augustin-Louis Cauchy.
Cauchy integral theorem (complex analysis) Cauchy–Hadamard theorem (complex analysis) Cauchy–Kowalevski theorem (partial differential equations) Cauchy's theorem ; Cauchy's theorem (finite groups) Cayley–Bacharach theorem (projective geometry) Cayley–Hamilton theorem (Linear algebra) Cayley–Salmon theorem (algebraic surfaces)
Several theorems are named after Augustin-Louis Cauchy. Cauchy theorem may mean: Cauchy's integral theorem in complex analysis, also Cauchy's integral formula; Cauchy's mean value theorem in real analysis, an extended form of the mean value theorem; Cauchy's theorem (group theory) Cauchy's theorem (geometry) on rigidity of convex polytopes
for the infinite series. Note that if the function () is increasing, then the function () is decreasing and the above theorem applies.. Many textbooks require the function to be positive, [1] [2] [3] but this condition is not really necessary, since when is negative and decreasing both = and () diverge.
Cauchy principal value; Cauchy problem. Abstract Cauchy problem; Cauchy process; Cauchy product; Cauchy's radical test; Cauchy–Rassias stability; Cauchy ratio test; Cauchy–Riemann equations; Cauchy–Riemann manifold; Cauchy's residue theorem; Cauchy–Schlömilch transformation; Cauchy–Schwarz inequality; Cauchy sequence. Uniformly ...
In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series.It depends on the quantity | |, where are the terms of the series, and states that the series converges absolutely if this quantity is less than one, but diverges if it is greater than one.