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Advanced Placement. Advanced Placement ( AP) Precalculus (also known as AP Precalc) is an Advanced Placement precalculus course and examination, offered by the College Board, in development since 2021 [ 1] and announced in May 2022. [ 2] The course debuted in the fall of 2023, with the first exam session taking place in May 2024.
The theorem is often given as this special case: If P is an injective polynomial function from an n-dimensional complex vector space to itself then P is bijective. That is, if P always maps distinct arguments to distinct values, then the values of P cover all of C n .
Unit testing, a.k.a. component or module testing, is a form of software testing by which isolated source code is tested to validate expected behavior. [ 1 ] Unit testing describes tests that are run at the unit-level to contrast testing at the integration or system level.
Colony-forming unit. In microbiology, a colony-forming unit ( CFU, cfu or Cfu) is a unit which estimates the number of microbial cells ( bacteria, fungi, viruses etc.) in a sample that are viable, able to multiply via binary fission under the controlled conditions. Counting with colony-forming units requires culturing the microbes and counts ...
In mathematics, Macdonald polynomials Pλ ( x; t, q) are a family of orthogonal symmetric polynomials in several variables, introduced by Macdonald in 1987. He later introduced a non-symmetric generalization in 1995. Macdonald originally associated his polynomials with weights λ of finite root systems and used just one variable t, but later ...
Standard normal table. In statistics, a standard normal table, also called the unit normal table or Z table, [ 1] is a mathematical table for the values of Φ, the cumulative distribution function of the normal distribution. It is used to find the probability that a statistic is observed below, above, or between values on the standard normal ...
Note that this will be true for all the orthogonal polynomials above, because each p n is constructed to be orthogonal to the other polynomials p j for j<n, and x k is in the span of that set. If we pick the n nodes x i to be the zeros of p n , then there exist n weights w i which make the Gaussian quadrature computed integral exact for all ...
The greatest common divisor polynomial g(x) of two polynomials a(x) and b(x) is defined as the product of their shared irreducible polynomials, which can be identified using the Euclidean algorithm. [128] The basic procedure is similar to that for integers.