![\lim_{x\to x0}f(x)](/img/math-symbols/lim.gif) |
limit |
limit value of a function |
![](/img/math-symbols/limit-example.png) |
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 |
![](/img/math-symbols/derivative1.gif) |
derivative |
derivative - Leibniz's notation |
d(3x3)/dx= 9x2 |
![](/img/math-symbols/derivative2.gif) |
second derivative |
derivative of derivative |
d2(3x3)/dx2= 18x |
![](/img/math-symbols/derivative-n.gif) |
nth derivative |
n times derivation |
![](/img/math-symbols/nth-derivative-example.png) |
![](/img/math-symbols/time_drivative1.gif) |
time derivative |
derivative by time - Newton's notation |
![](/img/math-symbols/time-derivative-ex.png) |
![](/img/math-symbols/time_drivative2.gif) |
time second derivative |
derivative of derivative |
![](/img/math-symbols/time-second-derivative.png) |
Dx y |
derivative |
derivative - Euler's notation |
Dx y for the first derivative |
Dx2y |
second derivative |
derivative of derivative |
Dx2y for the second derivative |
![](/img/math-symbols/partial-derivative.gif) |
partial derivative |
partial derivative |
∂(x2+y2)/∂x= 2x |
∫ |
integral |
opposite to derivation |
![](/img/math-symbols/integral.png) |
∬ |
double integral |
integration of function of 2 variables |
![](/img/math-symbols/double-integral-ex.png) |
∭ |
triple integral |
integration of function of 3 variables |
![](/img/math-symbols/closed-volume-integral.png) |
∮ |
closed contour / line integral |
closed contour / line integral |
![](/img/math-symbols/contour-integration.png) |
∯ |
closed surface integral |
closed surface integral |
|
∰ |
closed volume integral |
closed volume integral |
|
[a,b] |
closed interval |
closed interval |
[a,b] = {x | a ≤ x ≤ b} |
(a,b) |
open interval |
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) |
![](/img/math-symbols/v.gif) |
vector |
vector |
![](/img/math-symbols/vector-example.png) |
![](/img/math-symbols/uv.gif) |
unit vector |
unit vector |
![](/img/math-symbols/unit-vector-example.png) |
x * y |
convolution |
convolution |
y(t) = x(t)* h(t) |
![](/img/math-symbols/laplace-transform.gif) |
Laplace transform |
Laplace transform |
F(s) = {f (t)} |
![](/img/math-symbols/fourier-transform.gif) |
Fourier transform |
Fourier transform |
X(ω) = {f (t)} |
δ |
delta function |
delta function |
![](/img/math-symbols/delta-example.png) |
∞ |
lemniscate |
infinity symbol |
![](/img/math-symbols/lemniscate-ex.png) |