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2.2: The SAS Theorem. We have said that two triangles are congruent if all their correspond ing sides and angles are equal, However in some cases, it is possible to conclude that two triangles are congruent, with only partial information about their sides and angles. Suppose we are told that ABC A B C has ∠A = 53∘ ∠ A = 53 ∘, AB = 5 A ...
t. e. In statistics, the Gauss–Markov theorem (or simply Gauss theorem for some authors) [1] states that the ordinary least squares (OLS) estimator has the lowest sampling variance within the class of linear unbiased estimators, if the errors in the linear regression model are uncorrelated, have equal variances and expectation value of zero. [2]
2.11: Virial Theorem. The virial theorem is an important theorem for a system of moving particles both in classical physics and quantum physics. The Virial Theorem is useful when considering a collection of many particles and has a special importance to central-force motion. For a general system of mass points with position vectors ri r i and ...
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of ...
Noether’s theorem is the statement that for every continuous symmetry in a physical system, there exists a conservation law. A symmetry of a physical system, in the context of Noether’s theorem, means a transformation to the system that leaves its equations of motion unchanged. If this doesn’t tell you much yet, don’t worry.
Intermediate value theorem: Let be a continuous function defined on [,] and let be a number with () < < ().Then there exists some between and such that () =.. In mathematical analysis, the intermediate value theorem states that if is a continuous function whose domain contains the interval [a, b], then it takes on any given value between () and () at some point within the interval.
The Divergence Theorem. Let S be a piecewise, smooth closed surface that encloses solid E in space. Assume that S is oriented outward, and let ⇀ F be a vector field with continuous partial derivatives on an open region containing E (Figure 16.8.1 ). Then. ∭Ediv ⇀ FdV = ∬S ⇀ F ⋅ d ⇀ S.
