Discrete (i.e., incremental) version of infinitesimal calculus
This article is about the discrete version of calculus. It is not to be confused with Discretization in calculus.
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The word calculus is a Latin word, meaning originally "small pebble"; as such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation. Meanwhile, calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the study of continuous change.
Discrete calculus has two entry points, differential calculus and integral calculus. Differential calculus concerns incremental rates of change and the slopes of piece-wise linear curves. Integral calculus concerns accumulation of quantities and the areas under piece-wise constant curves. These two points of view are related to each other by the fundamental theorem of discrete calculus.
The study of the concepts of change starts with their discrete form. The development is dependent on a parameter, the increment of the independent variable. If we so choose, we can make the increment smaller and smaller and find the continuous counterparts of these concepts as limits. Informally, the limit of discrete calculus as is infinitesimal calculus. Even though it serves as a discrete underpinning of calculus, the main value of discrete calculus is in applications.
Discretecalculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of...
such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been...
In mathematics, the discrete exterior calculus (DEC) is the extension of the exterior calculus to discrete spaces including graphs, finite element meshes...
Digital data DiscretecalculusDiscrete system Discretization Normalized frequency Nyquist–Shannon sampling theorem Time-scale calculus "Digital Signal...
to the system of umbral calculus. Newton series expansions can be superior to Taylor series expansions when applied to discrete quantities like quantum...
and 1. Methods of calculus do not readily lend themselves to problems involving discrete variables. Especially in multivariable calculus, many models rely...
combinatorics. Topics in this area include: Discrete Laplace operator Discrete exterior calculusDiscretecalculusDiscrete Morse theory Topological combinatorics...
number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in ( Z / q...
which are piecewise linear finite elements, finite volumes, and discrete exterior calculus (PDF download: [1]). To facilitate computation, the Laplacian...
In mathematics, calculus on finite weighted graphs is a discretecalculus for functions whose domain is the vertex set of a graph with a finite number...
emergence of infinitesimal calculus in the 17th century. Analytic geometry continues to be a mainstay of pre-calculus and calculus curriculum. Another important...
and generating functions. During this period, calculus techniques were applied to approximate discrete problems by continuous ones. In the 18th century...
processes are respectively referred to as discrete-time and continuous-time stochastic processes. Discrete-time stochastic processes are considered easier...
called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus. The former concerns...
discrete and continuous settings. They can be used to construct systems of calculus called "weighted calculus" and "meta-calculus". In the discrete setting...
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations...
in any group G, powers bk can be defined for all integers k, and the discrete logarithm logb a is an integer k such that bk = a. In number theory, the...
Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number...
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables:...
additions to the family include the π-calculus, the ambient calculus, PEPA, the fusion calculus and the join-calculus. While the variety of existing process...
Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series...
In discretecalculus the indefinite sum operator (also known as the antidifference operator), denoted by ∑ x {\textstyle \sum _{x}} or Δ − 1 {\displaystyle...
applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This...
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...
theory Petri net theory Discrete event system specification Boolean differential calculus Markov chain Queueing theory Discrete-event simulation Concurrent...
Global Information
