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Concept
Coefficient
Summary
In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression. It may be a number (dimensionless), in which case it is known as a numerical factor. It may also be a constant with units of measurement, in which it is known as a constant multiplier. In general, coefficients may be any expression (including variables such as a, b and c). When the combination of variables and constants is not necessarily involved in a product, it may be called a parameter.
For example, the polynomial has coefficients 2, −1, and 3, and the powers of the variable in the polynomial have coefficient parameters , , and .
The , also known as constant term or simply constant is the quantity not attached to variables in an expression. For example, the constant coefficients of the expressions above are the number 3 and the parameter c, respectively.
The coefficient attached to the highest degree of the variable in a polynomial is referred to as the leading coefficient. For example, in the expressions above, the leading coefficients are 2 and a, respectively.
In the context of differential equations, an equation can often be written as equating to zero a polynomial in the unknown functions and their derivatives. In this case, the coefficients of the differential equation are the coefficients of this polynomial, and are generally non-constant functions. A coefficient is a constant coefficient when it is a constant function. For avoiding confusion, the coefficient that is not attached to unknown functions and their derivative is generally called the constant term rather the constant coefficient. In particular, in a linear differential equation with constant coefficient, the constant term is generally not supposed to be a constant function.
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression. For example, in the polynomial
with variables and , the first two terms have the coefficients 7 and −3. The third term 1.
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