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r unknown, to show how many times the latter is to be taken; as, 6x; bx; here 6 and b are coefficients of x.

or become a part of it, though not essential. [R.] Where no act of the will advenes as a coefficient. Coleridge.

A function involving the coefficients and the variables of a quantic, and such that when the quantic is lineally transformed the same function of the new variables and coefficients shall be equal to the old function multiplied by a factor. An invariant is a like function involving only the coefficients of the quantic.…

s; said of mechanism. Differential calculus. (Math.) See under Calculus. -- Differential coefficient, the limit of the ratio of the increment of a function of a variable to the increment of the variable itself, when these increments are made indefinitely small. -- Differential coupling, a form of slip coupling used i…

To obtain the differential, or differential coefficient, of; as, to differentiate an algebraic expression, or an equation.

Power of resistance to, or recovery from, depression or overwork. Coefficient of elasticity, the quotient of a stress (of a given kind), by the strain (of a given kind) which it produces; -- called also coefficient of resistance. -- Surface of elasticity (Geom.), the pedal surface of an ellipsoid (see Pedal); a surfac…

One of the variables of a quantic as distinguished from a coefficient.

ical harmonic analysis, a mathematical method, sometimes referred to as that of Laplace's Coefficients, which has for its object the expression of an arbitrary, periodic function of two independent variables, in the proper form for a large class of physical problems, involving arbitrary data, over a spherical surface,…

omplete equation (Alg.), an equation some of whose terms are wanting; or one in which the coefficient of some one or more of the powers of the unknown quantity is equal to 0.

alysis which has for its object the solution of indeterminate problems. -- Indeterminate coefficients (Math.), coefficients arbitrarily assumed for convenience of calculation, or to facilitate some artifice of analysis. Their values are subsequently determined. -- Indeterminate equation (Math.), an equation in which…

Capacity for induction; the coefficient of self-induction.

eration of finding the primitive function which has a given function for its differential coefficient. See Integral.

An invariable quantity; specifically, a function of the coefficients of one or more forms, which remains unaltered, when these undergo suitable linear transformations. J. J. Sylvester.

equated to zero is regarded as a function of the dependent variable and its differential coefficients. -- Linear equation (Math.), an equation of the first degree between two variables; -- so called because every such equation may be considered as representing a right line. -- Linear measure, the measurement of leng…

A quantity or coefficient, or constant, which expresses the measure of some specified force, property, or quality, as of elasticity, strength, efficiency, etc.; a parameter. Modulus of a machine, a formula expressing the work which a given machine can perform under the conditions involved in its construction; the relat…

f a higher order (or involves the equality of a greater number of successive differential coefficients of the ordinates of the curves taken at that point) than that of any other curve of the same kind.

flet is often supported by a partial petiole. Partial differentials, Partial differential coefficients, Partial differentiation, etc. (of a function of two or more variables), the differentials, differential coefficients, differentiation etc., of the function, upon the hypothesis that some of the variables are for the…

ctangular coordinates which determine the position of a point, such that its differential coefficients with respect to the coördinates are equal to the components of the force at the point considered; -- also called potential function, or force function. It is called also Newtonian potential when the force is directed…

ecimal. See under Decimal. -- Recurring series (Math.), an algebraic series in which the coefficients of the several terms can be expressed by means of certain preceding coefficients and constants in one uniform manner.

A numerical coefficient in any particular case of the binomial theorem. [Obs.]