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calculus. (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.
Look up calculus in Wiktionary, the free dictionary. In mathematics education, calculus is an abbreviation of both infinitesimal calculus and integral calculus, which denotes courses of elementary mathematical analysis. In Latin, the word calculus means “small pebble”, (the diminutive of calx, meaning "stone"), a meaning which still ...
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...
Calculus. The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations ...
v. t. e. In mathematics, the derivative is a fundamental tool that quantifies the sensitivity of change of a function 's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
In calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y, respectively, just as Δx and Δy represent finite increments of x and y, respectively. [ 1]
Differential calculus. Derivative. Notation. Newton's notation for differentiation. Leibniz's notation for differentiation. Simplest rules. Derivative of a constant. Sum rule in differentiation. Constant factor rule in differentiation.
In differential calculus, there is no single uniform notation for differentiation. Instead, various notations for the derivative of a function or variable have been proposed by various mathematicians. The usefulness of each notation varies with the context, and it is sometimes advantageous to use more than one notation in a given context.
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