Calculus Symbols

Symbol Symbol Name Meaning / definition Example
\lim_{x\to x0}f(x) 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 – Leibniz’s notation (3x3)’ = 9x2
y second derivative derivative of derivative (3x3)” = 18x
y(n) nth derivative n times derivation (3x3)(3) = 18
\frac{dy}{dx} derivative derivative – Lagrange’s notation d(3x3)/dx = 9x2
\frac{d^2y}{dx^2} second derivative derivative of derivative d2(3x3)/dx2 = 18x
\frac{d^ny}{dx^n} nth derivative n times derivation
\dot{y} time derivative derivative by time – Newton notation
time second derivative derivative of derivative
\frac{\partial f(x,y)}{\partial x} 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+biz*=abi z* = 3 + 2i
z complex conjugate z = a+biz = abi z = 3 + 2i
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