Definition, Meaning & Synonyms | English word CALCULUS

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Definitions of CALCULUS

1. (dated, countable) Calculation; computation.
2. (countable, mathematics) Any formal system in which symbolic expressions are manipulated according to fixed rules.
3. (uncountable, often, definite, the calculus) Differential calculus and integral calculus considered as a single subject; analysis.
4. (countable, medicine) A stony concretion that forms in a bodily organ.
5. (uncountable, dentistry) Deposits of calcium phosphate salts on teeth.
6. (countable) A decision-making method, especially one appropriate for a specialised realm.

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Examples of Using CALCULUS in a Sentence

• He was one of the first to rigorously state and prove the key theorems of calculus (thereby creating real analysis), pioneered the field complex analysis, and the study of permutation groups in abstract algebra.
• Antiderivatives are related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval where the function is Riemann integrable is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.
• 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.
• In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space.
• Critical point (mathematics), in calculus, a point where a function's derivative is either zero or nonexistent.
• Cartesian coordinates are named for René Descartes, whose invention of them in the 17th century revolutionized mathematics by allowing the expression of problems of geometry in terms of algebra and calculus.
• Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory).
• In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point.
• By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry.
• It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra.
• It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus.
• First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
• The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a shorter version of the proof, published as an article in 1930, titled "The completeness of the axioms of the functional calculus of logic" (in German)) is not easy to read today; it uses concepts and formalisms that are no longer used and terminology that is often obscure.
• Newton also made seminal contributions to optics, and shares credit with German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, though he developed calculus years before Leibniz.
• Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation.
• The Knights of the Lambda Calculus is a semi-fictional organization of expert Lisp and Scheme hackers.
• Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution.
• The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.
• For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions.
• This is the case in calculus, where, for example, the quotient of two functions is a partial function whose domain of definition cannot contain the zeros of the denominator; in this context, a partial function is generally simply called a.

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