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Culture · Geography · Health · History · Mathematics · Natural sciences · Philosophy · Religion · Society · Technology  Analysis is the process of breaking a complex topic or substance into smaller parts to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle, though analysis as a formal concept is a relatively recent development. As a formal concept, the method has variously been ascribed to Ibn al-Haytham, Descartes (Discourse on the Method), Galileo, and Newton, as a practical method of physical discovery. Calculus is a branch of mathematics, developed from algebra and geometry, built on two major complementary ideas. The first idea, called differential calculus, is about a vast generalization of the slope of a line. It is a theory about rates of change, defining differentiation. It permits velocity, acceleration, and the slope of a curve at a given point all to be discussed on a common conceptual basis. The second idea, called integral calculus, is about a vast generalization of area. It is a theory about accumulation of small, even infinitesimal, quantities, defining integration. Though originally motivated by area, it includes related concepts such as volume and even distance. The two concepts differentiation and integration define inverse operations in a sense made precise by the fundamental theorem of calculus. Therefore, in teaching calculus either may in fact be given priority, but the usual educational approach (nowadays) is to introduce differential calculus first.
The Mathematics WikiProject is the center for mathematics-related editing on Wikipedia. Join the discussion on the project's talk page. Project pages Subprojects Related projects  In complex dynamics, the Julia set of a holomorphic function informally consists of those points whose long-time behavior under repeated iteration of
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can change drastically under arbitrarily small perturbations. Above is a 3D slice of a 4D Julia set.
