Calculus and analysis math symbols and definitions.
| 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 | |
| ∬ | double integral | integration of function of 2 variables | |
| ∭ | triple integral | integration of function of 3 variables | |
| ∮ | 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 |
| Re(z) | real part of a complex number | z = a+bi → Re(z)=a | Re(3 - 2i) = 3 |
| Im(z) | imaginary part of a complex number | z = a+bi → Im(z)=b | Im(3 - 2i) = -2 |
| | z | | absolute value/magnitude of a complex number | |z| = |a+bi| = √(a2+b2) | |3 - 2i| = √13 |
| arg(z) | argument of a complex number | The angle of the radius in the complex plane | arg(3 + 2i) = 33.7° |
| ∇ | 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 |
