Calculus

As an extension of vector calculus operators to physics, engineering and tensor spaces, Grad, Div and Curl operators also are often associated with Tensor calculus as well as vector calculus.

Event calculus solution The event calculus uses terms for representing fluents, like the fluent calculus, but also has axioms constraining the value of fluents, like the successor state axioms.

See also portal * Applicative computing systems – Treatment of objects in the style of the lambda calculus * Binary lambda calculus – A version of lambda calculus with binary I/O, a binary encoding of terms, and a designated universal machine.

Semantics The fact that lambda calculus terms act as functions on other lambda calculus terms, and even on themselves, led to questions about the semantics of the lambda calculus.

Alternative calculus It is possible to define another version of propositional calculus, which defines most of the syntax of the logical operators by means of axioms, and which uses only one inference rule.

Although (untyped) lambda calculus is Turing-complete, simply typed lambda calculus is not.

A particular advantage of Kleene's tabular natural deduction systems is that he proves the validity of the inference rules for both propositional calculus and predicate calculus.

Basic and derived argument forms Proofs in propositional calculus One of the main uses of a propositional calculus, when interpreted for logical applications, is to determine relations of logical equivalence between propositional formulas.

Berkeley's key point in "The Analyst" was that Newton's calculus (and the laws of motion based in calculus) lacked rigorous theoretical foundations.

Following the work of Weierstrass, it eventually became common to base calculus on limits instead of infinitesimal quantities, though the subject is still occasionally called "infinitesimal calculus".

Geometric calculus Geometric calculus extends the formalism to include differentiation and integration including differential geometry and differential forms.

However, we know that the sequent calculus is complete with respect to natural deduction, so it is enough to show this unprovability in the sequent calculus.

In that year, Hermann Grassmann introduced the idea of a geometrical algebra in full generality as a certain calculus (analogous to the propositional calculus ) that encoded all of the geometrical information of a space.

Inverses in calculus Single-variable calculus is primarily concerned with functions that map real numbers to real numbers.

Lambda terms The syntax of the lambda calculus defines some expressions as valid lambda calculus expressions and some as invalid, just as some strings of characters are valid programs and some are not.

Learning must often follow a hierarchical scheme—to learn differential equations one must first learn calculus ; to learn calculus one must first learn elementary algebra ; and so on.

Newton was the first to apply calculus to general physics and Leibniz developed much of the notation used in calculus today.

Other logical calculi Propositional calculus is about the simplest kind of logical calculus in current use.

Physics makes particular use of calculus; all concepts in classical mechanics and electromagnetism are related through calculus.

Sequent calculus further The sequent calculus was developed to study the properties of natural deduction systems.