# Calculus Definitions

Browse our growing collection of calculus definitions:

## ARC

ARC an abbreviation of average rate of change is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value (Δy) divided by the change in the x-value (Δx) for two distinct points on the graph.

## Algorithm

An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point.

## Alternating Series

An alternating series is a series which alternates between positive and negative terms.

## Annulus

A annulus or washer is the region between two concentric circles which have different radii. The area of a annulus = π (R^{2} − r^{2})

## Area of an Ellipse

The area of an ellipse is calculated using a formula similar to that of a circle. For an ellipse with a semi-major and semi-minor axes the formula is: A = πxy where x represents the ellipses semi-major axes and y represents the semi-minor axis of the ellipse.

## Average Rate of Change

Average rate of change or ARC is the change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value (Δy) divided by the change in the x-value (Δx) for two distinct points on the graph.

## Delta (Δ, δ)

Delta (Δ, δ) is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4.

## Epsilon (Ε, ε)

Epsilon (Ε, ε) or lunate ϵ or Greek: έψιλον, is the fifth letter of the Greek alphabet, corresponding phonetically to a mid front unrounded vowel /e/. In the system of Greek numerals it also has the value five.

## Fixed

Fixed means that the object is regarded as fixed in the plane so that it may not be picked up and flipped if referring to a planar object. As a result, mirror images are not necessarily equivalent for fixed objects.

## Greek Alphabet

The Greek alphabet has been used to write the Greek language since the late ninth or early eighth century BC. It is derived from the earlier Phoenician alphabet, and was the first alphabetic script in history to have distinct letters for vowels as well as consonants.

## Integration

Integration is the process of computing or obtaining an integral, either a definite integral or an indefinite integral. A more archaic term for integration is quadrature.

## Jump Discontinuity

A jump discontinuity or step discontinuity is a discontinuity where the graph steps or jumps from one connected piece of the graph to another. It is a discontinuity where the limits from the left and right both exist but are not equal to each other.

## Sigma (Σ, σ)

Sigma (Σ, σ) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation.

## Step Discontinuity

A step discontinuity or jump discontinuity is a discontinuity where the graph steps or jumps from one connected piece of the graph to another.

## Theorem of Pappus

The theorem of Pappus or Pappus's theorem generally refer to several different theorems. They include Pappus's centroid theorem, the Pappus chain, Pappus's harmonic theorem, and Pappus's hexagon theorem.

## U-Substitution

U-Substitution also known as integration by substitution, or substitution method, is an integration method for evaluating integrals. Direct application of the fundamental theorem of calculus to find an antiderivative can be quite difficult, and integration by substitution can help simplify that task.

## Vector Calculus

Vector calculus or vector analysis is the use of calculus (limits, derivatives, and integrals) with two or more independent variables, or two or more dependent variables.

## Velocity

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

## Volume

Volume is the total amount of space enclosed or occupied in a solid. Volume generally has units of length and distance cubed (such as cm^{3}, in^{3}, m^{3} km^{3}, etc.)

## Washer

A washer or annulus is the region between two concentric circles which have different radii. The area of a washer = π (R^{2} − r^{2})

## Work

In physics, work is the product of force and displacement. A force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force.