A coefficient ((new) lat. Coefficiens / coëfficiens , a noun of the PPA from the lat. Coefficere "participate", formed by Franciscus Vieta ), also known as an initial number or pre- number, is a number or variable added to another arithmetic expression as a factor . The coefficient can be a parameter or a key figure (physics, economics). In analysis it appears in monomials .
In mathematics , a coefficient is a factor that belongs to a specific object such as a variable or a basis vector . Typically, objects and coefficients are indexed in the same order, so expressions like
result, with as the coefficient of the variable for each
Simple example: The coefficient of the term is .
Examples of important mathematical coefficients:
- Coefficients of the polynomial , especially the leading coefficient
- Binomial coefficient
- Taylor coefficients (see Taylor series )
- Fourier coefficients (see Fourier series )
- Coefficients of a power series or Laurent series , here in particular the residual
- Clebsch-Gordan coefficient
In physics , a coefficient is often, but not always, a quantity in the dimension number that describes a property of certain materials, bodies or systems. In older technical literature, coefficients are also called coefficients . Examples:
- Static friction coefficient , sliding friction coefficient
- Drag coefficient (" C w value")
- Heat transfer coefficient
Far from every physical constant of the dimension number is called a coefficient. Counterexamples:
- Fundamental natural constants such as the fine structure constant
- Ratios from similarity laws such as the Reynolds number
Examples of dimensional coefficients:
In stoichiometry , the stoichiometric coefficient indicates in a reaction equation how many particles or moles of a substance react with how many particles or moles of other substances. If the coefficient is 1, it is omitted.
- Example ( oxyhydrogen reaction ):
- Hydrogen and water have the stoichiometric coefficient 2 because
- 2 hydrogen molecules react with one oxygen molecule to form 2 water molecules
- 2 moles of hydrogen react with one mole of oxygen to form 2 moles of water.
Physical chemistry and biochemistry
- Binding coefficient (synonym coefficient of preferential interaction , English preferential interaction coefficient)
In sporting associations such. B. UEFA also has coefficients which clubs or teams rate based on their previous successes.