![]() And any function whose graph has no breaks along an interval can be approached with the integral calculus. More precisely, any function whose graph is smooth enough to have tangent lines can be investigated with differential calculus. ![]() The subject applies in many situations where the relevant functions and answers do not have formulas, which is the usual situation in real world applications. It must be realized, though, that calculus is not all about formulas. Many algebraic formulas in use for ballistics, heating and cooling, and other practical sciences were worked out through the use of calculus and then provided in handbooks for ease of use by non-mathematicians. Rather, it is whether the requisite formula is provided or not.įor example, finding the circumference of a circle does not require calculus provided the following is given: However, if one has only a related formula such as for the area of a circle, then calculus must be used to derive the formula for the circumference. Often what determines whether or not calculus is required to solve any given problem is not what ultimately needs to be accomplished. Therefore, in teaching calculus, either concept may be given priority, though the usual educational approach (nowadays) is to introduce differential calculus first. The two concepts, differentiation and integration, define inverse operations in a sense made precise by the fundamental theorem of calculus.
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