Subject: Calculus

Table Of Mathematical Symbols

Most Commonly Used Mathematical Symbols

Symbol

Common Name

Significance

Examples

Pronounced as

+

addition; positive sign

symbolizes addition of quantities

4+6 = 10

add; summed with; plus


-

subtraction;
negative sign

subtraction of quantities;
-7 means the negative of 7

4 - 6 = - 2

minus; negative;
diminished; taken out with

\times

\cdot

multiplication; cross product
multiplication; dot product

signifies the multiplication of two quantities;

signifies the cross and dot product of vectors

2\times3=6; A\times B = C

2\cdot3 = 6; A\cdot B = C

times; cross

multiplied by; dot

\div
\

division (Obelus)

means the quotient or division of quantities

6\div 2 = 3
6\3 = 2

divide; divided by
over; quotient of

\pm
\mp

plus-minus
minus-plus

shortcut for the {addition,subtraction} of quantities;

4\pm 2 = 6, 2
4\mp 2 = 2, 6

plus-minus
minus-plus

=

equal sign

signifies equality and the sameness

A is equal to B -> A = B

is equal to; is the same as

\neq

inequality

a ≠ b means that a and b do not represent the same thing or value.

1 ≠ 2

is not equal to; does not equal

>
<

strict inequality

when a > b, it signifies that a is greater than b.
when a < b, it signifies that a is less than b.

2 > 1
1 < 2

greater than
less than; lesser than

>>
<<

very strict inequality

when a >> b, it signifies a is much greater than b.
when a << b, it signifies that a is much less than b.

100000 >> 1
1 << 100000

is much greater than
is much less than

\geq

\leq


inequality

when a \geq b, it signifies a is greater than or equal to b.
when a \leq b, it signifies that a is less than or equal to b.

6,7 \geq 6

6,7 \leq 7

is greater than or equal to
is less than or equal to

\sqrt{}

square root

\sqrt{a} means a nonnegative number when multiplied by itself results a.

\sqrt{4} = 2

the square root of

!

factorial

x! means the product 1 2 ... x.

6! = 1 2 3 4 5 6 = 720

factorial

\approx

approximately equal

signifies an approximated equality between two quantities;
a\approx b means a is approximately equal to b.

g\approx 9.8 m/s*s

is approximately equal to

\cong

congruence

signifies that a two quantities has the same measurement;
a\cong b means a has the same measurement to b.

a\cong b

is congruent to

\int

indefinite integral;
anti-derivative

∫ f(x) dx means a function whose derivative is f.

∫(x^2 + 1) dx = x3/3 + x + C

indefinite integral of;
the antiderivative of

\oint

contour integral;
closed-line integral

used to denote a single integration over a closed curve or loop.

If C is a Jordan curve about 0, then \oint_{C} \frac{1}{z}dz = 2\pi i

contour integral of



gradient;

divergence;
curl

\nabla f(x,y,z) is the partial derivatives of f with respect to x, y, and z.
\nabla \cdot \bar{f} = \frac{\partial f_{x}}{\partial x} + \frac{\partial f_{y}}{\partial y}+ \frac{\partial f_{z}}{\partial z}
\nabla \times \bar{f} = i\left ( \frac{\partial f_{z}}{\partial z}-\frac{\partial f_{y}}{\partial y} \right ) + j\left ( \frac{\partial f_{x}}{\partial x}-\frac{\partial f_{z}}{\partial z} \right ) + k\left ( \frac{\partial f_{y}}{\partial y}-\frac{\partial f_{x}}{\partial x} \right )

\nabla \cdot \bar{f} = \frac{\partial f_{x}}{\partial x} + \frac{\partial f_{y}}{\partial y}+ \frac{\partial f_{z}}{\partial z}

\nabla \times \bar{f} = i\left ( \frac{\partial f_{z}}{\partial z}-\frac{\partial f_{y}}{\partial y} \right ) + j\left ( \frac{\partial f_{x}}{\partial x}-\frac{\partial f_{z}}{\partial z} \right ) + k\left ( \frac{\partial f_{y}}{\partial y}-\frac{\partial f_{x}}{\partial x} \right )

del, gradient of;

del dot, divergence of;
curl

\partial

partial derivative

\frac{\partial f}{\partial x} denotes partial derivative of f with respect to x.

Assume: f(x,y)=x^2 +2y,
then \frac{\partial f}{\partial x} = 2x

partial

\Delta

delta

used to denote a non-infinitesimal change in a value

\Delta f means a very small change in f.

delta, change in


\delta

Dirac delta function
Kronecker delta function

if x=0, then \delta (x)=\infty , if x\neq 0, then \delta (x)=\infty ;
if m=n, then \delta_{m,n}=1 , if m\neq n, then \delta_{m,n}=0 ;

\delta (x)

\delta_{m,n}

Dirac delta of

Kronecker delta of


\pi


pi

a constant widely used in many formulas especially circles; obtained by dividing the circumference to the diameter of a circle.


A_{s} = 4\pi r^2

pi
3.14159