| Symbol |
Symbol Name |
Meaning / definition |
Example |
 |
limit |
limit value of a function |
| ε |
epsilon |
represents a very small number, near zero |
ε → 0 |
| e |
e constant / Euler’s number |
e = 2.718281828… |
e = lim (1+1/x)x , x→∞ |
| y ‘ |
derivative |
derivative – Lagrange’s notation |
(3x3)’ = 9x2 |
| y ” |
second derivative |
derivative of derivative |
(3x3)” = 18x |
| y(n) |
nth derivative |
n times derivation |
(3x3)(3) = 18 |
 |
derivative |
derivative – Leibniz’s notation |
d(3x3)/dx = 9x2 |
 |
second derivative |
derivative of derivative |
d2(3x3)/dx2 = 18x |
 |
nth derivative |
n times derivation |
|
 |
time derivative |
derivative by time – Newton’s notation |
|
 |
time second derivative |
derivative of derivative |
|
| Dx y |
derivative |
derivative – Euler’s notation |
|
| Dx2y |
second derivative |
derivative of derivative |
|
 |
partial derivative |
∂(x2+y2)/∂x = 2x |
|
| ∫ |
integral |
opposite to derivation |
∫ f(x)dx |
| ∫∫ |
double integral |
integration of function of 2 variables |
∫∫ f(x,y)dxdy |
| ∫∫∫ |
triple integral |
integration of function of 3 variables |
∫∫∫ f(x,y,z)dxdydz |
| ∮ |
closed contour / line integral |
|
|
| ∯ |
closed surface integral |
|
|
| ∰ |
closed volume integral |
|
|
| [a,b] |
closed interval |
[a,b] = {x | a ≤ x ≤ b} |
|
| (a,b) |
open interval |
(a,b) = {x | a < x < b} |
|
| i |
imaginary unit |
i ≡ √-1 |
z = 3 + 2i |
| z* |
complex conjugate |
z = a+bi → z*=a–bi |
z* = 3 – 2i |
| z |
complex conjugate |
z = a+bi → z = a–bi |
z = 3 – 2i |
| ∇ |
nabla / del |
gradient / divergence operator |
∇f (x,y,z) |
 |
vector |
 |
unit vector |
|
|
| x * y |
convolution |
y(t) = x(t) * h(t) |
|
 |
Laplace transform |
F(s) = {f (t)} |
|
 |
Fourier transform |
X(ω) = {f (t)} |
|
| δ |
delta function |
|
|
| ∞ |
lemniscate |
infinity symbol |
|