## 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 (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
Dy 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] = {| 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 f (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