# Calculus & analysis symbols

Calculus:
The branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus.

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→∞
derivative derivative – Leibniz’s notation (3x3)’ = 9x2
second derivative derivative of derivative (3x3)” = 18x
y(n) nth derivative n times derivation (3x3)(3) = 18
derivative derivative – Lagrange’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 notation
time 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] = {| a  x  b}
(a,b) open interval (a,b) = {| a < x < b}
i imaginary unit i ≡ √-1 z = 3 + 2i
z* complex conjugate = a+bi → z*=abi z* = 3 + 2i
z complex conjugate = a+bi → = abi z = 3 + 2i
nabla / del gradient / divergence operator (x,y,z)
vector
unit vector
* y convolution y(t) = x(t) * h(t)
Laplace transform F(s) = {(t)}
Fourier transform X(ω) = {(t)}
δ delta function
lemniscate infinity symbol