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area under curve Let a curve be given by arithmetic sum The sum of an arithmetic
N
y = f(x), a ≤ x ≤ b. The area A under this sequence (a + nd).
n=0
curve from a to b is given by the integral
arity The number of arguments of a relation.
b

A = f(x)dx .
a array A display of objects in some regular
arrangements, as a rectangular array or matrix
Argand diagram The basic idea of complex
in which numbers are displayed in rows and
numbers is credited to Jean Robert Argand, a columns, or an arrangement of statistical data in
Swiss mathematician (1768–1822). An Argand order of increasing (or decreasing) magnitude.
diagram is a rectangular coordinate system in
which the complex number x + iy is represented array index In a rectangular array such as a
by the point whose coordinates are x and y. The matrix the element in the ith row and jth column
x-axis is called real axis and the y-axis is called is indexed as a .
ij
imaginary axis.
artificial intelligence A branch of computer
argument The collection of elements satis- science dealing with the simulation of intelligent
fying some relation r is called the set of argu- behavior of computers.
ments of r.
ascending sequence A sequence {a } is
n
argument of complex number See ampli- called ascending (increasing) if each term is
tude of a complex number. greater than the previous term, i.e., a ≥ a .
n n−1
If a >a n−1 then it is called monotone ascend-
n
arithmetic Thestudyofthepositiveintegers
ing/increasing.
1, 2, 3, 4, 5, ... under the operations of addition,
subtraction, multiplication, and division.
ASCII American Standard Code for
Information Interchange. A code for represent-
arithmetic difference The arithmetic dif- ing alphanumeric information.
ference of two numbers a and b is |a − b|.
Ascoli Giulio Ascoli (1843–1896), Italian
arithmetic division To determine the arith-

analyst.
a
metic quotient of two nonnegative integers a
b
and b, where [x] is the greatest integer, which is
Ascoli’s theorem Let {f } be a family of
n
not bigger than x.
uniformly bounded equicontinuous functions on
[0, 1]. Then some subsequence {f } converges
arithmetic mean The arithmetic mean of n n(i)
uniformly on [0, 1].
numbers a ,a , ..., a is
n
1
2
a + a + ··· + a n assembler A computer program that auto-
2
1
x = .
n matically converts instructions written in assem-
bly language into computer language.
arithmetic progression A sequence of
numbers a ,a , ..., a , ... in which each follow- assembly Computation of a finite element
2
1
n
ing number is obtained from the preceding num- stiffness matrix A from the element matrices A K
ber by adding a given number r, i.e., a = a + belonging to the cells K of the underlying mesh
1
n
(n − 1)r. ; . The general formula is
h
arithmetic quotient See arithmetic divi- T
A = I A I ,
K K
K
sion.
K∈; h
arithmetic sequence A sequence a, (a + where the I K are rectangular matrices reflect-
d), (a + 2d), ··· ,(a + nd), ··· , in which each ing the association of local and global degrees
term is the arithmetic mean of its neighbors. of freedom.
© 2003 by CRC Press LLC