# Table of Calculus & Analysis Symbols with Examples   ## Math Calculus & Analysis with Examples

Symbol Symbol Name Symbol Meaning 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 Dx y for the first derivative
Dx2y second derivative derivative of derivative Dx2y for the second derivative partial 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 contour / line integral 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+biz*=a-bi z* = 3 + 2i
z complex conjugate z = a+biz =a-bi z = 3 + 2i
nabla / del gradient / divergence operator f (x,y,z) vector vector  unit vector unit vector x * y convolution convolution y(t) = x(t)* h(t) Laplace transform Laplace transform F(s) = {f (t)} Fourier transform Fourier transform X(ω) = {f (t)}
δ delta function delta function lemniscate infinity symbol  