differential calculus
    n 1: the part of calculus that deals with the variation of a
         function with respect to changes in the independent
         variable (or variables) by means of the concepts of
         derivative and differential [syn: differential calculus,
         method of fluxions]

differential \dif`fer*en"tial\, a. [Cf. F. diff['e]rentiel.]
   1. Relating to or indicating a difference; creating a
      difference; discriminating; special; as, differential
      characteristics; differential duties; a differential rate.
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            For whom he produced differential favors. --Motley.
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   2. (Math.) Of or pertaining to a differential, or to
      differentials.
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   3. (Mech.) Relating to differences of motion or leverage;
      producing effects by such differences; said of mechanism.
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   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 in
      light machinery to regulate at pleasure the velocity of
      the connected shaft.

   Differential duties (Polit. Econ.), duties which are not
      imposed equally upon the same products imported from
      different countries.

   Differential galvanometer (Elec.), a galvanometer having
      two coils or circuits, usually equal, through which
      currents passing in opposite directions are measured by
      the difference of their effect upon the needle.

   Differential gearing, a train of toothed wheels, usually an
      epicyclic train, so arranged as to constitute a
      differential motion.

   Differential motion, a mechanism in which a simple
      differential combination produces such a change of motion
      or force as would, with ordinary compound arrangements,
      require a considerable train of parts. It is used for
      overcoming great resistance or producing very slow or very
      rapid motion.

   Differential pulley. (Mach.)
      (a) A portable hoisting apparatus, the same in principle
          as the differential windlass.
      (b) A hoisting pulley to which power is applied through a
          differential gearing.

   Differential screw, a compound screw by which a motion is
      produced equal to the difference of the motions of the
      component screws.

   Differential thermometer, a thermometer usually with a
      U-shaped tube terminating in two air bulbs, and containing
      a colored liquid, used for indicating the difference
      between the temperatures to which the two bulbs are
      exposed, by the change of position of the colored fluid,
      in consequence of the different expansions of the air in
      the bulbs. A graduated scale is attached to one leg of the
      tube.

   Differential windlass, or Chinese windlass, a windlass
      whose barrel has two parts of different diameters. The
      hoisting rope winds upon one part as it unwinds from the
      other, and a pulley sustaining the weight to be lifted
      hangs in the bight of the rope. It is an ancient example
      of a differential motion.
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Calculus \Cal"cu*lus\, n.; pl. Calculi. [L, calculus. See
   Calculate, and Calcule.]
   1. (Med.) Any solid concretion, formed in any part of the
      body, but most frequent in the organs that act as
      reservoirs, and in the passages connected with them; as,
      biliary calculi; urinary calculi, etc.
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   2. (Math.) A method of computation; any process of reasoning
      by the use of symbols; any branch of mathematics that may
      involve calculation.
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   Barycentric calculus, a method of treating geometry by
      defining a point as the center of gravity of certain other
      points to which co["e]fficients or weights are ascribed.
      

   Calculus of functions, that branch of mathematics which
      treats of the forms of functions that shall satisfy given
      conditions.

   Calculus of operations, that branch of mathematical logic
      that treats of all operations that satisfy given
      conditions.

   Calculus of probabilities, the science that treats of the
      computation of the probabilities of events, or the
      application of numbers to chance.

   Calculus of variations, a branch of mathematics in which
      the laws of dependence which bind the variable quantities
      together are themselves subject to change.

   Differential calculus, a method of investigating
      mathematical questions by using the ratio of certain
      indefinitely small quantities called differentials. The
      problems are primarily of this form: to find how the
      change in some variable quantity alters at each instant
      the value of a quantity dependent upon it.

   Exponential calculus, that part of algebra which treats of
      exponents.

   Imaginary calculus, a method of investigating the relations
      of real or imaginary quantities by the use of the
      imaginary symbols and quantities of algebra.

   Integral calculus, a method which in the reverse of the
      differential, the primary object of which is to learn from
      the known ratio of the indefinitely small changes of two
      or more magnitudes, the relation of the magnitudes
      themselves, or, in other words, from having the
      differential of an algebraic expression to find the
      expression itself.
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