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# Calculus & Analysis Symbols

Calculus & Analysis Symbols – List of all calculus & analysis symbols and signs – meaning and examples.

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)/dx= 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
Dx2y second derivative derivative of derivative
partial derivative ∂(x2+y2)/∂= 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+bi → z*=abi z* = 3 + 2i
z complex conjugate z = a+bi → z 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

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