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; |
subtraction of quantities; |
4 - 6 = - 2 |
minus; negative; |
\times |
multiplication; cross product |
signifies the multiplication of two quantities; |
2\times3=6; A\times B = C |
times; cross |
\div |
division (Obelus) |
means the quotient or division of quantities |
6\div 2 = 3 |
divide; divided by |
\pm |
plus-minus |
shortcut for the {addition,subtraction} of quantities; |
4\pm 2 = 6, 2 |
plus-minus |
= |
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. |
2 > 1 |
greater than |
>> |
very strict inequality |
when a >> b, it signifies a is much greater than b. |
100000 >> 1 |
is much greater than |
\geq |
|
when a \geq b, it signifies a is greater than or equal to b. |
6,7 \geq 6 |
is greater 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; |
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 |
is congruent to |
\int |
indefinite integral; |
∫ f(x) dx means a function whose derivative is f. |
∫(x^2 + 1) dx = x3/3 + x + C |
indefinite integral of; |
\oint |
contour 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; |
\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} |
del, gradient of; |
\partial |
partial derivative |
\frac{\partial f}{\partial x} denotes partial derivative of f with respect to x. |
Assume: f(x,y)=x^2 +2y, |
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 |
|
Dirac delta function |
if x=0, then \delta (x)=\infty , if x\neq 0, then \delta (x)=\infty ; |
\delta (x) |
Dirac delta of |
|
|
a constant widely used in many formulas especially circles; obtained by dividing the circumference to the diameter of a circle. |
|
pi |