1) In a mathematical equation, a coefficient is a constant by which a variable is multiplied. Consider the following equations:

3 *x* ^{2} + 5 *x* - 3 = 0

*ax* ^{3} + *by* ^{2} = *z*

The values 3 and 5 in the first equation are coefficients of *x* , a variable. In the second equation, if *a* and *b* are constants, then *a* is a coefficient of *x* ^{3} , and *b* is a coefficient of *y* ^{2} . It is customary to use lower-case, italic letters from the first half of the alphabet to represent constants whose values are not specified numerically. Lower-case, italic letters from the second half of the alphabet generally represent variables.

2) In physics and engineering, a coefficient is a quantitative expression of a specific property of matter, or of a phenomenon. Consider an electronic component whose value changes with temperature. It is tested and found to have a resistance of 100 ohm s at a temperature of +20 degrees Celsius (°C), and a resistance of 101 ohms at a temperature of +70 °C. This is the equivalent of a change in resistance of +1 ohm for a temperature change of +50 °C, or +0.02 ohm per degree Celsius. Between temperatures of +20 °C and +70 °C, therefore, this component has a temperature coefficient of +0.02 ohm per degree Celsius, assuming the resistance-versus-temperature function is linear over that range of temperatures.

*This was last updated in*September 2005

*Posted by:*Margaret Rouse

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