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Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals ", it has two major branches, differential calculus and integral calculus .
Fundamental theorem of calculus; Integration by parts; Inverse chain rule method; Integration by substitution. Tangent half-angle substitution; Differentiation under the integral sign; Trigonometric substitution; Partial fractions in integration. Quadratic integral; Proof that 22/7 exceeds π; Trapezium rule; Integral of the secant function ...
Regge calculus is a formalism which chops up a Lorentzian manifold into discrete 'chunks' (four-dimensional simplicial blocks) and the block edge lengths are taken as the basic variables. A discrete version of the Einstein–Hilbert action is obtained by considering so-called deficit angles of these blocks, a zero deficit angle corresponding to ...
The covariant derivative is a generalization of the directional derivative from vector calculus. As with the directional derivative, the covariant derivative is a rule, which takes as its inputs: (1) a vector, u, (along which the derivative is taken) defined at a point P, and (2) a vector field, v, defined in a neighborhood of P.
Precalculus prepares students for calculus somewhat differently from the way that pre-algebra prepares students for algebra. While pre-algebra often has extensive coverage of basic algebraic concepts, precalculus courses might see only small amounts of calculus concepts, if at all, and often involves covering algebraic topics that might not have been given attention in earlier algebra courses.
The case n = −1 required the invention ... The fundamental theorem of calculus is the statement that differentiation and ... a computer algebra system rule-based ...
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
(From Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus) [8] is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. Cavalieri's principle
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