CALCULUS OF FINITE DIFFERENCES
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A collection of rules or theorems applicable to calculations performed with certain defined classes of magnitudes. Conceive two magnitudes connected in such a manner that a change in the one necessitates a corresponding change in the other, e.g. the radius and the area of a circle. Any corresponding changes which these two magnitudes undergo are called their differences. If these differences are finite, a collection of theorems may be formed having reference to the relations existing between them, and such a collection of theorems is called the C. of finite differences. If the differences are indefinitely small, such as would occur when the change takes place continuously, we have the Differential C. The theorem of the Integral C. relates to the total finite result of a continuous change, the rate of which at each point is known, i.e. to the determination of functions from their differential coefficients. These and similar calculi are commonly carried out into numerous details; and, in particular, most treatises on the Differential and Integral C. explain the applications of these calculi to questions of geometry, etc. It is not unusual to speak of the differential and integral calculus as The C, on account of its numerous applications to physical questions, most changes in nature being continuous. (For C. of variation, vide ISO.)
By Henry Percy Smith
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