mean value theorem
noun1
Mathematics, Sciences Any of various theorems that saliently concern mean values.
- Several mean value theorems in the theory of elasticity have appeared in the recent literature[…].1964, J. H. Bramble, L. E. Payne, Some Mean Value Theorems in Electrostatics: Journal of the Society for Industrial and Applied Mathematics, volume 12, page 105:
- 1984 [Nauka, Moscow], Sergey Ermakov, V. V. Nekrutkin (authors and translators), A. S. Sipin (author), Random Processes for Classical Equations of Mathematical Physics, [1984, С. М. Ермаков, В. В. Некруткин, А. С. Сипин, Случайные процессы для решения классических уравнений математической физики], 1989, Kluwer, Softcover Reprint, page xiii, For parabolic equations (Section 5.1) and for the exterior Dirichlet problem (Section 5.2), it is possible to apply the well known mean value theorems.
3 more examples
- However, Anton switches, unannounced, to another conceptualization in justifying the Fundamental Theorem - he bases it on the mean value theorem for integrals.1994, Patrick W. Thompson, “Images of Rate and Operational Understanding of the Fundamental Theorem of Calculus”, in Paul Cobb, editor, Learning Mathematics, Kluwer, page 167:
- We prove mean value theorems in the context of integrals which are analogous to the ones studied in Chapter 5.2013, Elimhan Mahmudov, Single Variable Differential and Integral Calculus: Mathematical Analysis, Springer, page 259:
- The mean value theorem for derivatives provides an important link between the derivative of f on an interval and the behavior of f over the interval.2013, Peter D. Lax, Maria Shea Terrell, Calculus With Applications, Springer, page 171:
- Derived terms
- Cauchy's mean value theorem, extended mean value theorem, Gauss's mean value theorem
- Related terms
- intermediate value theorem