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The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
A branch of physics that studies atoms as isolated systems of electrons and an atomic nucleus. Compare nuclear physics. atomic structure atomic weight (A) The sum total of protons (or electrons) and neutrons within an atom. audio frequency A periodic vibration whose frequency is in the band audible to the average human, the human hearing range.
An extension that splits a family of polynomials: every root of the minimal polynomial of an element of E over F is also in E. Separable extension An algebraic extension in which the minimal polynomial of every element of E over F is a separable polynomial, that is, has distinct roots. [11] Galois extension A normal, separable field extension.
This eigenvalue problem is called the Hermite equation, although the term is also used for the closely related equation ″ ′ =. whose solution is uniquely given in terms of physicist's Hermite polynomials in the form () = (), where denotes a constant, after imposing the boundary condition that u should be polynomially bounded at infinity.
A monomial is a polynomial with one term while two- and three-term polynomials are called binomials and trinomials. The degree of a polynomial is the maximal value (among its terms) of the sum of the exponents of the variables (4 in the above example). [32] Polynomials of degree one are called linear polynomials.
A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials. One problem of particular interest is that of approximating a function in a computer mathematical library, using operations that can be performed on the ...
(Note that it makes sense for such an equation to have a polynomial solution. Each term in the equation is a polynomial, and the degrees are consistent.) This is a Sturm–Liouville type of equation. Such equations generally have singularities in their solution functions f except for particular values of λ.
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.