## Calculus & analysis symbols

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 | (3x^{3})' = 9x^{2} |

y '' | second derivative | derivative of derivative | (3x^{3})'' = 18x |

y^{(n)} | nth derivative | n times derivation | (3x^{3})^{(3)} = 18 |

derivative | derivative - Leibniz's notation | d(3x^{3})/dx = 9x^{2} | |

second derivative | derivative of derivative | d^{2}(3x^{3})/dx^{2} = 18x | |

nth derivative | n times derivation | ||

time derivative | derivative by time - Newton's notation | ||

time second derivative | derivative of derivative | ||

D_{x }y | derivative | derivative - Euler's notation | |

D_{x}^{2}y | second derivative | derivative of derivative | |

partial derivative | ∂(x^{2}+y^{2})/∂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 |

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| = √(a^{2}+b^{2}) | |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 |