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Foundation Mathematics for the Physical Sciences by K. F. Riley, M. P. Hobson

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4

Integral calculus

As indicated at the start of the previous chapter, the differential calculus and its complement, the integral calculus, together form the most widely used tool for the analysis of physical systems. The link that connects the two is that they both deal with the effects of vanishingly small changes in related quantities; one seeks to obtain the ratio of two such changes, the other uses such a ratio to calculate the variation in one of the quantities resulting from a change in the other.

Any change in the value of any one property (or variable) of a physical system almost always results in the values of some or all of its other properties being altered; in general, the size of each consequential change depends upon the current ...

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