Calculus

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Calculus is Latin for pebble, and has a number of meanings in English:

In mathematics and computer science

Calculus, in its most general sense, is any method or system of calculation. To modern theoreticians the answer to the question "what is a calculus?" is: any systematic way of reasoning.^[1]

• Calculus, short for Differential and Integral Calculus, which investigates motion and rates of change. The denotation "the Calculus" is sometimes used to distinguish this from other mathematical meanings.
• Precalculus, a family of mathematical topics that prepare students to begin to study differential and integral calculus.
• the calculus of sums and differences, also called the finite-difference calculus, a discrete analogue of the Calculus.
• In symbolic logic:
  • the propositional calculus, which specify the rules of inference governing the logic of propositions.
  • the predicate calculus, which specify the rules of inference governing the logic of predicates.
  • a proof calculus, a framework for expressing systems of logical inference.
  • the sequent calculus, a proof calculus for first-order logic.
• Bondi k-calculus, a method used in relativity theory
• Domain relational calculus, a calculus for the relational data model.
• Functional calculus, a way to apply various types of functions to operators.
• Join calculus, a theoretical model for distributed programming.
• Lambda calculus, a formulation of the theory of reflexive functions that has deep connections to computational theory.
• Matrix calculus, a specialized notation for multivariable calculus over spaces of matrices.
• Modal μ-calculus, a common temporal logic used by formal verification methods such as model checking.
• Non-standard calculus, an approach to infinitesimal calculus using Robinson's infinitesimals.
• Pi-calculus, a formulation of the theory of concurrent, communicating processes, invented by Robin Milner.
• Refinement calculus, a way of refining models of programs into efficient programs.
• Rho calculus, introduced as a general means to uniformly integrate rewriting and lambda calculus.
• Tuple calculus, a calculus for the relational data model, inspired the SQL language.
• Umbral calculus, the combinatorics of certain operations on polynomials.
• the calculus of variations, the study of extremal functionals.
• Vector calculus (also called vector analysis), comprising specialized notations for multivariable analysis of vectors in an inner-product space.

Other meanings

• Calculus (dental), deposits of calcium phosphate salts on teeth, also known as tartar.
• Calculus (medicine), a stone formed in the body such as a gall stone or kidney stone.
• Battlefield calculus, military factoring of all known factors into the decision making and action planning process
• Calculus, a spider genus (Oonopidae).
• Caseolus calculus, a species of small land snails.
• Professor Cuthbert Calculus, a fictional character in the series The Adventures of Tintin
• Calculus of negligence, in tort law, a legal standard to determine if a duty of care has been breached.

References

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